Proofs of the stability and convergence of a weakened weak method using PIM shape functions
Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothi...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yue, J.H. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016transfer abstract |
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| Schlagwörter: |
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| Umfang: |
19 |
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| Übergeordnetes Werk: |
Enthalten in: Growth and welfare implications of sector-specific innovations - Güner, İlhan ELSEVIER, 2022, an international journal, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:72 ; year:2016 ; number:4 ; pages:933-951 ; extent:19 |
| Links: |
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| DOI / URN: |
10.1016/j.camwa.2016.06.002 |
|---|
| Katalog-ID: |
ELV040107884 |
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| 520 | |a Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. | ||
| 520 | |a Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. | ||
| 650 | 7 | |a Stability |2 Elsevier | |
| 650 | 7 | |a G space |2 Elsevier | |
| 650 | 7 | |a Smoothed point interpolation method |2 Elsevier | |
| 650 | 7 | |a Weakened weak form |2 Elsevier | |
| 650 | 7 | |a Convergence |2 Elsevier | |
| 700 | 1 | |a Li, M. |4 oth | |
| 700 | 1 | |a Liu, G.R. |4 oth | |
| 700 | 1 | |a Niu, R.P. |4 oth | |
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10.1016/j.camwa.2016.06.002 doi GBVA2016014000003.pica (DE-627)ELV040107884 (ELSEVIER)S0898-1221(16)30334-0 DE-627 ger DE-627 rakwb eng 510 004 510 DE-600 004 DE-600 330 VZ 83.03 bkl 83.10 bkl Yue, J.H. verfasserin aut Proofs of the stability and convergence of a weakened weak method using PIM shape functions 2016transfer abstract 19 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. Stability Elsevier G space Elsevier Smoothed point interpolation method Elsevier Weakened weak form Elsevier Convergence Elsevier Li, M. oth Liu, G.R. oth Niu, R.P. oth Enthalten in Elsevier Science Güner, İlhan ELSEVIER Growth and welfare implications of sector-specific innovations 2022 an international journal Amsterdam [u.a.] (DE-627)ELV008987521 volume:72 year:2016 number:4 pages:933-951 extent:19 https://doi.org/10.1016/j.camwa.2016.06.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 83.03 Methoden und Techniken der Volkswirtschaft VZ 83.10 Wirtschaftstheorie: Allgemeines VZ AR 72 2016 4 933-951 19 045F 510 |
| spelling |
10.1016/j.camwa.2016.06.002 doi GBVA2016014000003.pica (DE-627)ELV040107884 (ELSEVIER)S0898-1221(16)30334-0 DE-627 ger DE-627 rakwb eng 510 004 510 DE-600 004 DE-600 330 VZ 83.03 bkl 83.10 bkl Yue, J.H. verfasserin aut Proofs of the stability and convergence of a weakened weak method using PIM shape functions 2016transfer abstract 19 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. Stability Elsevier G space Elsevier Smoothed point interpolation method Elsevier Weakened weak form Elsevier Convergence Elsevier Li, M. oth Liu, G.R. oth Niu, R.P. oth Enthalten in Elsevier Science Güner, İlhan ELSEVIER Growth and welfare implications of sector-specific innovations 2022 an international journal Amsterdam [u.a.] (DE-627)ELV008987521 volume:72 year:2016 number:4 pages:933-951 extent:19 https://doi.org/10.1016/j.camwa.2016.06.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 83.03 Methoden und Techniken der Volkswirtschaft VZ 83.10 Wirtschaftstheorie: Allgemeines VZ AR 72 2016 4 933-951 19 045F 510 |
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10.1016/j.camwa.2016.06.002 doi GBVA2016014000003.pica (DE-627)ELV040107884 (ELSEVIER)S0898-1221(16)30334-0 DE-627 ger DE-627 rakwb eng 510 004 510 DE-600 004 DE-600 330 VZ 83.03 bkl 83.10 bkl Yue, J.H. verfasserin aut Proofs of the stability and convergence of a weakened weak method using PIM shape functions 2016transfer abstract 19 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. Stability Elsevier G space Elsevier Smoothed point interpolation method Elsevier Weakened weak form Elsevier Convergence Elsevier Li, M. oth Liu, G.R. oth Niu, R.P. oth Enthalten in Elsevier Science Güner, İlhan ELSEVIER Growth and welfare implications of sector-specific innovations 2022 an international journal Amsterdam [u.a.] (DE-627)ELV008987521 volume:72 year:2016 number:4 pages:933-951 extent:19 https://doi.org/10.1016/j.camwa.2016.06.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 83.03 Methoden und Techniken der Volkswirtschaft VZ 83.10 Wirtschaftstheorie: Allgemeines VZ AR 72 2016 4 933-951 19 045F 510 |
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10.1016/j.camwa.2016.06.002 doi GBVA2016014000003.pica (DE-627)ELV040107884 (ELSEVIER)S0898-1221(16)30334-0 DE-627 ger DE-627 rakwb eng 510 004 510 DE-600 004 DE-600 330 VZ 83.03 bkl 83.10 bkl Yue, J.H. verfasserin aut Proofs of the stability and convergence of a weakened weak method using PIM shape functions 2016transfer abstract 19 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. Stability Elsevier G space Elsevier Smoothed point interpolation method Elsevier Weakened weak form Elsevier Convergence Elsevier Li, M. oth Liu, G.R. oth Niu, R.P. oth Enthalten in Elsevier Science Güner, İlhan ELSEVIER Growth and welfare implications of sector-specific innovations 2022 an international journal Amsterdam [u.a.] (DE-627)ELV008987521 volume:72 year:2016 number:4 pages:933-951 extent:19 https://doi.org/10.1016/j.camwa.2016.06.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 83.03 Methoden und Techniken der Volkswirtschaft VZ 83.10 Wirtschaftstheorie: Allgemeines VZ AR 72 2016 4 933-951 19 045F 510 |
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10.1016/j.camwa.2016.06.002 doi GBVA2016014000003.pica (DE-627)ELV040107884 (ELSEVIER)S0898-1221(16)30334-0 DE-627 ger DE-627 rakwb eng 510 004 510 DE-600 004 DE-600 330 VZ 83.03 bkl 83.10 bkl Yue, J.H. verfasserin aut Proofs of the stability and convergence of a weakened weak method using PIM shape functions 2016transfer abstract 19 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. Stability Elsevier G space Elsevier Smoothed point interpolation method Elsevier Weakened weak form Elsevier Convergence Elsevier Li, M. oth Liu, G.R. oth Niu, R.P. oth Enthalten in Elsevier Science Güner, İlhan ELSEVIER Growth and welfare implications of sector-specific innovations 2022 an international journal Amsterdam [u.a.] (DE-627)ELV008987521 volume:72 year:2016 number:4 pages:933-951 extent:19 https://doi.org/10.1016/j.camwa.2016.06.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 83.03 Methoden und Techniken der Volkswirtschaft VZ 83.10 Wirtschaftstheorie: Allgemeines VZ AR 72 2016 4 933-951 19 045F 510 |
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Proofs of the stability and convergence of a weakened weak method using PIM shape functions |
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Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. |
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Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. |
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Recently, the smoothed point interpolation method (S-PIM) regarded as a weakened weak ( W 2 ) formulation method has been developed for solving engineering mechanics problems. It works well with distorted meshes. The G space theory offers the theoretical base for all the W 2 methods that use smoothing operations. In this paper, we first prove mathematically that if a function is of Lipschitz continuity and its interpolated function is established using PIM shape functions, then the interpolated function belongs to a G h , 0 s space. Our proofs work for smoothing operations that are the node-based, cell-based and a mixture of both smoothing domains. In addition, when mesh is refined under a given regularity condition, a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy, meaning that the interpolation error norm approaches to zero. Therefore, the stability and convergence of a W 2 method using PIM shape functions and G space theory can be ensured. |
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