Design and analysis of the Extended Hybrid High-Order method for the Poisson problem
Abstract We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is formulated by enriching the local polynomial space...
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| Autor*in: |
Yemm, Liam [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Advances in computational mathematics - Springer US, 1993, 48(2022), 4 vom: 02. Juli |
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| Übergeordnetes Werk: |
volume:48 ; year:2022 ; number:4 ; day:02 ; month:07 |
| Links: |
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| DOI / URN: |
10.1007/s10444-022-09958-y |
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OLC2079065122 |
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| 520 | |a Abstract We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is formulated by enriching the local polynomial spaces with appropriate singular functions. Via a detailed error analysis, the method is shown to converge optimally in both discrete and continuous energy norms. Some tests are conducted in two dimensions for singularities arising from irregular geometries in the domain. The numerical simulations illustrate the established error estimates, and show the method to be a significant improvement over a standard Hybrid High-Order method. | ||
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| 650 | 4 | |a Polytopal meshes | |
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10.1007/s10444-022-09958-y doi (DE-627)OLC2079065122 (DE-He213)s10444-022-09958-y-p DE-627 ger DE-627 rakwb eng 510 VZ Yemm, Liam verfasserin (orcid)0000-0003-2120-4048 aut Design and analysis of the Extended Hybrid High-Order method for the Poisson problem 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2022 Abstract We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is formulated by enriching the local polynomial spaces with appropriate singular functions. Via a detailed error analysis, the method is shown to converge optimally in both discrete and continuous energy norms. Some tests are conducted in two dimensions for singularities arising from irregular geometries in the domain. The numerical simulations illustrate the established error estimates, and show the method to be a significant improvement over a standard Hybrid High-Order method. Hybrid High-Order methods Enriched scheme Error analysis Singular solution Polytopal meshes Enthalten in Advances in computational mathematics Springer US, 1993 48(2022), 4 vom: 02. Juli (DE-627)165684380 (DE-600)1164256-7 (DE-576)038869179 1019-7168 nnns volume:48 year:2022 number:4 day:02 month:07 https://doi.org/10.1007/s10444-022-09958-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 GBV_ILN_4266 AR 48 2022 4 02 07 |
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10.1007/s10444-022-09958-y doi (DE-627)OLC2079065122 (DE-He213)s10444-022-09958-y-p DE-627 ger DE-627 rakwb eng 510 VZ Yemm, Liam verfasserin (orcid)0000-0003-2120-4048 aut Design and analysis of the Extended Hybrid High-Order method for the Poisson problem 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2022 Abstract We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is formulated by enriching the local polynomial spaces with appropriate singular functions. Via a detailed error analysis, the method is shown to converge optimally in both discrete and continuous energy norms. Some tests are conducted in two dimensions for singularities arising from irregular geometries in the domain. The numerical simulations illustrate the established error estimates, and show the method to be a significant improvement over a standard Hybrid High-Order method. Hybrid High-Order methods Enriched scheme Error analysis Singular solution Polytopal meshes Enthalten in Advances in computational mathematics Springer US, 1993 48(2022), 4 vom: 02. Juli (DE-627)165684380 (DE-600)1164256-7 (DE-576)038869179 1019-7168 nnns volume:48 year:2022 number:4 day:02 month:07 https://doi.org/10.1007/s10444-022-09958-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 GBV_ILN_4266 AR 48 2022 4 02 07 |
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10.1007/s10444-022-09958-y doi (DE-627)OLC2079065122 (DE-He213)s10444-022-09958-y-p DE-627 ger DE-627 rakwb eng 510 VZ Yemm, Liam verfasserin (orcid)0000-0003-2120-4048 aut Design and analysis of the Extended Hybrid High-Order method for the Poisson problem 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2022 Abstract We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is formulated by enriching the local polynomial spaces with appropriate singular functions. Via a detailed error analysis, the method is shown to converge optimally in both discrete and continuous energy norms. Some tests are conducted in two dimensions for singularities arising from irregular geometries in the domain. The numerical simulations illustrate the established error estimates, and show the method to be a significant improvement over a standard Hybrid High-Order method. Hybrid High-Order methods Enriched scheme Error analysis Singular solution Polytopal meshes Enthalten in Advances in computational mathematics Springer US, 1993 48(2022), 4 vom: 02. Juli (DE-627)165684380 (DE-600)1164256-7 (DE-576)038869179 1019-7168 nnns volume:48 year:2022 number:4 day:02 month:07 https://doi.org/10.1007/s10444-022-09958-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 GBV_ILN_4266 AR 48 2022 4 02 07 |
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10.1007/s10444-022-09958-y doi (DE-627)OLC2079065122 (DE-He213)s10444-022-09958-y-p DE-627 ger DE-627 rakwb eng 510 VZ Yemm, Liam verfasserin (orcid)0000-0003-2120-4048 aut Design and analysis of the Extended Hybrid High-Order method for the Poisson problem 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2022 Abstract We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is formulated by enriching the local polynomial spaces with appropriate singular functions. Via a detailed error analysis, the method is shown to converge optimally in both discrete and continuous energy norms. Some tests are conducted in two dimensions for singularities arising from irregular geometries in the domain. The numerical simulations illustrate the established error estimates, and show the method to be a significant improvement over a standard Hybrid High-Order method. Hybrid High-Order methods Enriched scheme Error analysis Singular solution Polytopal meshes Enthalten in Advances in computational mathematics Springer US, 1993 48(2022), 4 vom: 02. Juli (DE-627)165684380 (DE-600)1164256-7 (DE-576)038869179 1019-7168 nnns volume:48 year:2022 number:4 day:02 month:07 https://doi.org/10.1007/s10444-022-09958-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 GBV_ILN_4266 AR 48 2022 4 02 07 |
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10.1007/s10444-022-09958-y doi (DE-627)OLC2079065122 (DE-He213)s10444-022-09958-y-p DE-627 ger DE-627 rakwb eng 510 VZ Yemm, Liam verfasserin (orcid)0000-0003-2120-4048 aut Design and analysis of the Extended Hybrid High-Order method for the Poisson problem 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2022 Abstract We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is formulated by enriching the local polynomial spaces with appropriate singular functions. Via a detailed error analysis, the method is shown to converge optimally in both discrete and continuous energy norms. Some tests are conducted in two dimensions for singularities arising from irregular geometries in the domain. The numerical simulations illustrate the established error estimates, and show the method to be a significant improvement over a standard Hybrid High-Order method. Hybrid High-Order methods Enriched scheme Error analysis Singular solution Polytopal meshes Enthalten in Advances in computational mathematics Springer US, 1993 48(2022), 4 vom: 02. Juli (DE-627)165684380 (DE-600)1164256-7 (DE-576)038869179 1019-7168 nnns volume:48 year:2022 number:4 day:02 month:07 https://doi.org/10.1007/s10444-022-09958-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 GBV_ILN_4266 AR 48 2022 4 02 07 |
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Abstract We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is formulated by enriching the local polynomial spaces with appropriate singular functions. Via a detailed error analysis, the method is shown to converge optimally in both discrete and continuous energy norms. Some tests are conducted in two dimensions for singularities arising from irregular geometries in the domain. The numerical simulations illustrate the established error estimates, and show the method to be a significant improvement over a standard Hybrid High-Order method. © The Author(s) 2022 |
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Abstract We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is formulated by enriching the local polynomial spaces with appropriate singular functions. Via a detailed error analysis, the method is shown to converge optimally in both discrete and continuous energy norms. Some tests are conducted in two dimensions for singularities arising from irregular geometries in the domain. The numerical simulations illustrate the established error estimates, and show the method to be a significant improvement over a standard Hybrid High-Order method. © The Author(s) 2022 |
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Abstract We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is formulated by enriching the local polynomial spaces with appropriate singular functions. Via a detailed error analysis, the method is shown to converge optimally in both discrete and continuous energy norms. Some tests are conducted in two dimensions for singularities arising from irregular geometries in the domain. The numerical simulations illustrate the established error estimates, and show the method to be a significant improvement over a standard Hybrid High-Order method. © The Author(s) 2022 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2079065122</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230506052512.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">221220s2022 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10444-022-09958-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2079065122</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10444-022-09958-y-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Yemm, Liam</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-2120-4048</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Design and analysis of the Extended Hybrid High-Order method for the Poisson problem</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2022</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. 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The numerical simulations illustrate the established error estimates, and show the method to be a significant improvement over a standard Hybrid High-Order method.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hybrid High-Order methods</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Enriched scheme</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Error analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Singular solution</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polytopal meshes</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Advances in computational mathematics</subfield><subfield code="d">Springer US, 1993</subfield><subfield code="g">48(2022), 4 vom: 02. 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