Two-level iterative finite element methods for the stationary natural convection equations with different viscosities based on three corrections
Abstract This paper considers the two-level iterative finite element methods for the steady natural convection equations under some uniqueness conditions with the Simple-, Oseen- and Newton-type corrections. Firstly, the stability and convergence of the one-level iterative finite element methods are...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Zhang, Huifang [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Anmerkung: |
© The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Computational and applied mathematics - Berlin : Springer, 2003, 42(2022), 1 vom: 15. Dez. |
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| Übergeordnetes Werk: |
volume:42 ; year:2022 ; number:1 ; day:15 ; month:12 |
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| DOI / URN: |
10.1007/s40314-022-02147-z |
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| Katalog-ID: |
SPR048887056 |
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| 520 | |a Abstract This paper considers the two-level iterative finite element methods for the steady natural convection equations under some uniqueness conditions with the Simple-, Oseen- and Newton-type corrections. Firstly, the stability and convergence of the one-level iterative finite element methods are analyzed under some restrictions on physical parameters. Secondly, under the strong uniqueness condition, we develop the two-level finite element method with Simple, Oseen and Newton iterations of m times on the coarse mesh %$\tau _H%$ with mesh size H, and then, the considered problem is linearized in three correction schemes with the Simple, Oseen and Newton corrections one time on the fine grid %$\tau _h%$ with mesh size %$h\ll H%$ based on the obtained iterative solutions. From the theoretical point of view, the results obtained by the two-level iterative methods have the same precision as those obtained by the one-level method which mesh sizes satisfy %$h={\mathcal {O}}(H^2)%$ and the iterative steps are greater than some constants. Thirdly, the stability and convergence of one-level Oseen iterative scheme with respect to the mesh size and the iterative time m are provided under a weak uniqueness condition. Finally, some numerical experiments are designed to confirm the established theoretical findings and verify the performance of the proposed numerical schemes. | ||
| 650 | 4 | |a The natural convection equations |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Two-level methods |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Iterative method |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Stability |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Convergence |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Chen, Chuanjun |4 aut | |
| 700 | 1 | |a Zhang, Tong |4 aut | |
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10.1007/s40314-022-02147-z doi (DE-627)SPR048887056 (SPR)s40314-022-02147-z-e DE-627 ger DE-627 rakwb eng Zhang, Huifang verfasserin aut Two-level iterative finite element methods for the stationary natural convection equations with different viscosities based on three corrections 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This paper considers the two-level iterative finite element methods for the steady natural convection equations under some uniqueness conditions with the Simple-, Oseen- and Newton-type corrections. Firstly, the stability and convergence of the one-level iterative finite element methods are analyzed under some restrictions on physical parameters. Secondly, under the strong uniqueness condition, we develop the two-level finite element method with Simple, Oseen and Newton iterations of m times on the coarse mesh %$\tau _H%$ with mesh size H, and then, the considered problem is linearized in three correction schemes with the Simple, Oseen and Newton corrections one time on the fine grid %$\tau _h%$ with mesh size %$h\ll H%$ based on the obtained iterative solutions. From the theoretical point of view, the results obtained by the two-level iterative methods have the same precision as those obtained by the one-level method which mesh sizes satisfy %$h={\mathcal {O}}(H^2)%$ and the iterative steps are greater than some constants. Thirdly, the stability and convergence of one-level Oseen iterative scheme with respect to the mesh size and the iterative time m are provided under a weak uniqueness condition. Finally, some numerical experiments are designed to confirm the established theoretical findings and verify the performance of the proposed numerical schemes. The natural convection equations (dpeaa)DE-He213 Two-level methods (dpeaa)DE-He213 Iterative method (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Convergence (dpeaa)DE-He213 Chen, Chuanjun aut Zhang, Tong aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 42(2022), 1 vom: 15. Dez. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:42 year:2022 number:1 day:15 month:12 https://dx.doi.org/10.1007/s40314-022-02147-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 42 2022 1 15 12 |
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10.1007/s40314-022-02147-z doi (DE-627)SPR048887056 (SPR)s40314-022-02147-z-e DE-627 ger DE-627 rakwb eng Zhang, Huifang verfasserin aut Two-level iterative finite element methods for the stationary natural convection equations with different viscosities based on three corrections 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This paper considers the two-level iterative finite element methods for the steady natural convection equations under some uniqueness conditions with the Simple-, Oseen- and Newton-type corrections. Firstly, the stability and convergence of the one-level iterative finite element methods are analyzed under some restrictions on physical parameters. Secondly, under the strong uniqueness condition, we develop the two-level finite element method with Simple, Oseen and Newton iterations of m times on the coarse mesh %$\tau _H%$ with mesh size H, and then, the considered problem is linearized in three correction schemes with the Simple, Oseen and Newton corrections one time on the fine grid %$\tau _h%$ with mesh size %$h\ll H%$ based on the obtained iterative solutions. From the theoretical point of view, the results obtained by the two-level iterative methods have the same precision as those obtained by the one-level method which mesh sizes satisfy %$h={\mathcal {O}}(H^2)%$ and the iterative steps are greater than some constants. Thirdly, the stability and convergence of one-level Oseen iterative scheme with respect to the mesh size and the iterative time m are provided under a weak uniqueness condition. Finally, some numerical experiments are designed to confirm the established theoretical findings and verify the performance of the proposed numerical schemes. The natural convection equations (dpeaa)DE-He213 Two-level methods (dpeaa)DE-He213 Iterative method (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Convergence (dpeaa)DE-He213 Chen, Chuanjun aut Zhang, Tong aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 42(2022), 1 vom: 15. Dez. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:42 year:2022 number:1 day:15 month:12 https://dx.doi.org/10.1007/s40314-022-02147-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 42 2022 1 15 12 |
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10.1007/s40314-022-02147-z doi (DE-627)SPR048887056 (SPR)s40314-022-02147-z-e DE-627 ger DE-627 rakwb eng Zhang, Huifang verfasserin aut Two-level iterative finite element methods for the stationary natural convection equations with different viscosities based on three corrections 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This paper considers the two-level iterative finite element methods for the steady natural convection equations under some uniqueness conditions with the Simple-, Oseen- and Newton-type corrections. Firstly, the stability and convergence of the one-level iterative finite element methods are analyzed under some restrictions on physical parameters. Secondly, under the strong uniqueness condition, we develop the two-level finite element method with Simple, Oseen and Newton iterations of m times on the coarse mesh %$\tau _H%$ with mesh size H, and then, the considered problem is linearized in three correction schemes with the Simple, Oseen and Newton corrections one time on the fine grid %$\tau _h%$ with mesh size %$h\ll H%$ based on the obtained iterative solutions. From the theoretical point of view, the results obtained by the two-level iterative methods have the same precision as those obtained by the one-level method which mesh sizes satisfy %$h={\mathcal {O}}(H^2)%$ and the iterative steps are greater than some constants. Thirdly, the stability and convergence of one-level Oseen iterative scheme with respect to the mesh size and the iterative time m are provided under a weak uniqueness condition. Finally, some numerical experiments are designed to confirm the established theoretical findings and verify the performance of the proposed numerical schemes. The natural convection equations (dpeaa)DE-He213 Two-level methods (dpeaa)DE-He213 Iterative method (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Convergence (dpeaa)DE-He213 Chen, Chuanjun aut Zhang, Tong aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 42(2022), 1 vom: 15. Dez. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:42 year:2022 number:1 day:15 month:12 https://dx.doi.org/10.1007/s40314-022-02147-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 42 2022 1 15 12 |
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10.1007/s40314-022-02147-z doi (DE-627)SPR048887056 (SPR)s40314-022-02147-z-e DE-627 ger DE-627 rakwb eng Zhang, Huifang verfasserin aut Two-level iterative finite element methods for the stationary natural convection equations with different viscosities based on three corrections 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This paper considers the two-level iterative finite element methods for the steady natural convection equations under some uniqueness conditions with the Simple-, Oseen- and Newton-type corrections. Firstly, the stability and convergence of the one-level iterative finite element methods are analyzed under some restrictions on physical parameters. Secondly, under the strong uniqueness condition, we develop the two-level finite element method with Simple, Oseen and Newton iterations of m times on the coarse mesh %$\tau _H%$ with mesh size H, and then, the considered problem is linearized in three correction schemes with the Simple, Oseen and Newton corrections one time on the fine grid %$\tau _h%$ with mesh size %$h\ll H%$ based on the obtained iterative solutions. From the theoretical point of view, the results obtained by the two-level iterative methods have the same precision as those obtained by the one-level method which mesh sizes satisfy %$h={\mathcal {O}}(H^2)%$ and the iterative steps are greater than some constants. Thirdly, the stability and convergence of one-level Oseen iterative scheme with respect to the mesh size and the iterative time m are provided under a weak uniqueness condition. Finally, some numerical experiments are designed to confirm the established theoretical findings and verify the performance of the proposed numerical schemes. The natural convection equations (dpeaa)DE-He213 Two-level methods (dpeaa)DE-He213 Iterative method (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Convergence (dpeaa)DE-He213 Chen, Chuanjun aut Zhang, Tong aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 42(2022), 1 vom: 15. Dez. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:42 year:2022 number:1 day:15 month:12 https://dx.doi.org/10.1007/s40314-022-02147-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 42 2022 1 15 12 |
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10.1007/s40314-022-02147-z doi (DE-627)SPR048887056 (SPR)s40314-022-02147-z-e DE-627 ger DE-627 rakwb eng Zhang, Huifang verfasserin aut Two-level iterative finite element methods for the stationary natural convection equations with different viscosities based on three corrections 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This paper considers the two-level iterative finite element methods for the steady natural convection equations under some uniqueness conditions with the Simple-, Oseen- and Newton-type corrections. Firstly, the stability and convergence of the one-level iterative finite element methods are analyzed under some restrictions on physical parameters. Secondly, under the strong uniqueness condition, we develop the two-level finite element method with Simple, Oseen and Newton iterations of m times on the coarse mesh %$\tau _H%$ with mesh size H, and then, the considered problem is linearized in three correction schemes with the Simple, Oseen and Newton corrections one time on the fine grid %$\tau _h%$ with mesh size %$h\ll H%$ based on the obtained iterative solutions. From the theoretical point of view, the results obtained by the two-level iterative methods have the same precision as those obtained by the one-level method which mesh sizes satisfy %$h={\mathcal {O}}(H^2)%$ and the iterative steps are greater than some constants. Thirdly, the stability and convergence of one-level Oseen iterative scheme with respect to the mesh size and the iterative time m are provided under a weak uniqueness condition. Finally, some numerical experiments are designed to confirm the established theoretical findings and verify the performance of the proposed numerical schemes. The natural convection equations (dpeaa)DE-He213 Two-level methods (dpeaa)DE-He213 Iterative method (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Convergence (dpeaa)DE-He213 Chen, Chuanjun aut Zhang, Tong aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 42(2022), 1 vom: 15. Dez. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:42 year:2022 number:1 day:15 month:12 https://dx.doi.org/10.1007/s40314-022-02147-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 42 2022 1 15 12 |
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper considers the two-level iterative finite element methods for the steady natural convection equations under some uniqueness conditions with the Simple-, Oseen- and Newton-type corrections. Firstly, the stability and convergence of the one-level iterative finite element methods are analyzed under some restrictions on physical parameters. Secondly, under the strong uniqueness condition, we develop the two-level finite element method with Simple, Oseen and Newton iterations of m times on the coarse mesh %$\tau _H%$ with mesh size H, and then, the considered problem is linearized in three correction schemes with the Simple, Oseen and Newton corrections one time on the fine grid %$\tau _h%$ with mesh size %$h\ll H%$ based on the obtained iterative solutions. From the theoretical point of view, the results obtained by the two-level iterative methods have the same precision as those obtained by the one-level method which mesh sizes satisfy %$h={\mathcal {O}}(H^2)%$ and the iterative steps are greater than some constants. Thirdly, the stability and convergence of one-level Oseen iterative scheme with respect to the mesh size and the iterative time m are provided under a weak uniqueness condition. Finally, some numerical experiments are designed to confirm the established theoretical findings and verify the performance of the proposed numerical schemes.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">The natural convection equations</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Two-level methods</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Iterative method</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stability</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convergence</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Chen, Chuanjun</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhang, Tong</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Computational and applied mathematics</subfield><subfield code="d">Berlin : Springer, 2003</subfield><subfield code="g">42(2022), 1 vom: 15. 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Two-level iterative finite element methods for the stationary natural convection equations with different viscosities based on three corrections The natural convection equations (dpeaa)DE-He213 Two-level methods (dpeaa)DE-He213 Iterative method (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Convergence (dpeaa)DE-He213 |
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two-level iterative finite element methods for the stationary natural convection equations with different viscosities based on three corrections |
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Two-level iterative finite element methods for the stationary natural convection equations with different viscosities based on three corrections |
| abstract |
Abstract This paper considers the two-level iterative finite element methods for the steady natural convection equations under some uniqueness conditions with the Simple-, Oseen- and Newton-type corrections. Firstly, the stability and convergence of the one-level iterative finite element methods are analyzed under some restrictions on physical parameters. Secondly, under the strong uniqueness condition, we develop the two-level finite element method with Simple, Oseen and Newton iterations of m times on the coarse mesh %$\tau _H%$ with mesh size H, and then, the considered problem is linearized in three correction schemes with the Simple, Oseen and Newton corrections one time on the fine grid %$\tau _h%$ with mesh size %$h\ll H%$ based on the obtained iterative solutions. From the theoretical point of view, the results obtained by the two-level iterative methods have the same precision as those obtained by the one-level method which mesh sizes satisfy %$h={\mathcal {O}}(H^2)%$ and the iterative steps are greater than some constants. Thirdly, the stability and convergence of one-level Oseen iterative scheme with respect to the mesh size and the iterative time m are provided under a weak uniqueness condition. Finally, some numerical experiments are designed to confirm the established theoretical findings and verify the performance of the proposed numerical schemes. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract This paper considers the two-level iterative finite element methods for the steady natural convection equations under some uniqueness conditions with the Simple-, Oseen- and Newton-type corrections. Firstly, the stability and convergence of the one-level iterative finite element methods are analyzed under some restrictions on physical parameters. Secondly, under the strong uniqueness condition, we develop the two-level finite element method with Simple, Oseen and Newton iterations of m times on the coarse mesh %$\tau _H%$ with mesh size H, and then, the considered problem is linearized in three correction schemes with the Simple, Oseen and Newton corrections one time on the fine grid %$\tau _h%$ with mesh size %$h\ll H%$ based on the obtained iterative solutions. From the theoretical point of view, the results obtained by the two-level iterative methods have the same precision as those obtained by the one-level method which mesh sizes satisfy %$h={\mathcal {O}}(H^2)%$ and the iterative steps are greater than some constants. Thirdly, the stability and convergence of one-level Oseen iterative scheme with respect to the mesh size and the iterative time m are provided under a weak uniqueness condition. Finally, some numerical experiments are designed to confirm the established theoretical findings and verify the performance of the proposed numerical schemes. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract This paper considers the two-level iterative finite element methods for the steady natural convection equations under some uniqueness conditions with the Simple-, Oseen- and Newton-type corrections. Firstly, the stability and convergence of the one-level iterative finite element methods are analyzed under some restrictions on physical parameters. Secondly, under the strong uniqueness condition, we develop the two-level finite element method with Simple, Oseen and Newton iterations of m times on the coarse mesh %$\tau _H%$ with mesh size H, and then, the considered problem is linearized in three correction schemes with the Simple, Oseen and Newton corrections one time on the fine grid %$\tau _h%$ with mesh size %$h\ll H%$ based on the obtained iterative solutions. From the theoretical point of view, the results obtained by the two-level iterative methods have the same precision as those obtained by the one-level method which mesh sizes satisfy %$h={\mathcal {O}}(H^2)%$ and the iterative steps are greater than some constants. Thirdly, the stability and convergence of one-level Oseen iterative scheme with respect to the mesh size and the iterative time m are provided under a weak uniqueness condition. Finally, some numerical experiments are designed to confirm the established theoretical findings and verify the performance of the proposed numerical schemes. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Two-level iterative finite element methods for the stationary natural convection equations with different viscosities based on three corrections |
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https://dx.doi.org/10.1007/s40314-022-02147-z |
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Chen, Chuanjun Zhang, Tong |
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Chen, Chuanjun Zhang, Tong |
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10.1007/s40314-022-02147-z |
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|
| score |
7.3971157 |