Reliable Residual-Based Error Estimation for the Finite Cell Method
Abstract In this work, the reliability of a residual-based error estimator for the Finite Cell method is established. The error estimator is suitable for the application of hp-adaptive finite elements and allows for Neumann boundary conditions on curved boundaries. The reliability proof of the error...
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| Autor*in: |
Di Stolfo, Paolo [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of scientific computing - Springer US, 1986, 87(2021), 1 vom: 23. Feb. |
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| Übergeordnetes Werk: |
volume:87 ; year:2021 ; number:1 ; day:23 ; month:02 |
| Links: |
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| DOI / URN: |
10.1007/s10915-021-01417-y |
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OLC2123934089 |
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| 520 | |a Abstract In this work, the reliability of a residual-based error estimator for the Finite Cell method is established. The error estimator is suitable for the application of hp-adaptive finite elements and allows for Neumann boundary conditions on curved boundaries. The reliability proof of the error estimator relies on standard arguments of residual-based a posteriori error control, but includes several modifications with respect to the error contributions associated with the volume residuals as well as the jumps across inner edges and Neumann boundary parts. Important ingredients of the proof are Stein’s extension theorem and a modified trace theorem which estimates the norm of the trace on (curved) boundary parts in terms of the local mesh size and polynomial degree. The efficiency of the error estimator is also considered by discussing an artificial example which yields an efficiency index depending on the mesh-family parameter h. Numerical experiments on more realistic domains, however, suggest global efficiency with the occurrence of a large overestimation on only few cut elements. In the experiments the reliability of the error estimator is demonstrated for h- and p-uniform as well as for hp-geometric and h-adaptive refinements driven by the error estimator. The practical applicability of the error estimator is also studied for a 3D problem with a non-smooth solution. | ||
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| 650 | 4 | |a Residual-based | |
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| 700 | 1 | |a Schröder, Andreas |4 aut | |
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10.1007/s10915-021-01417-y doi (DE-627)OLC2123934089 (DE-He213)s10915-021-01417-y-p DE-627 ger DE-627 rakwb eng 004 VZ 11 ssgn Di Stolfo, Paolo verfasserin (orcid)0000-0001-5735-5644 aut Reliable Residual-Based Error Estimation for the Finite Cell Method 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2021 Abstract In this work, the reliability of a residual-based error estimator for the Finite Cell method is established. The error estimator is suitable for the application of hp-adaptive finite elements and allows for Neumann boundary conditions on curved boundaries. The reliability proof of the error estimator relies on standard arguments of residual-based a posteriori error control, but includes several modifications with respect to the error contributions associated with the volume residuals as well as the jumps across inner edges and Neumann boundary parts. Important ingredients of the proof are Stein’s extension theorem and a modified trace theorem which estimates the norm of the trace on (curved) boundary parts in terms of the local mesh size and polynomial degree. The efficiency of the error estimator is also considered by discussing an artificial example which yields an efficiency index depending on the mesh-family parameter h. Numerical experiments on more realistic domains, however, suggest global efficiency with the occurrence of a large overestimation on only few cut elements. In the experiments the reliability of the error estimator is demonstrated for h- and p-uniform as well as for hp-geometric and h-adaptive refinements driven by the error estimator. The practical applicability of the error estimator is also studied for a 3D problem with a non-smooth solution. A posteriori error estimation Finite Cell method Residual-based hp-FEM Schröder, Andreas aut Enthalten in Journal of scientific computing Springer US, 1986 87(2021), 1 vom: 23. Feb. (DE-627)129217549 (DE-600)56055-8 (DE-576)065121945 0885-7474 nnns volume:87 year:2021 number:1 day:23 month:02 https://doi.org/10.1007/s10915-021-01417-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 87 2021 1 23 02 |
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10.1007/s10915-021-01417-y doi (DE-627)OLC2123934089 (DE-He213)s10915-021-01417-y-p DE-627 ger DE-627 rakwb eng 004 VZ 11 ssgn Di Stolfo, Paolo verfasserin (orcid)0000-0001-5735-5644 aut Reliable Residual-Based Error Estimation for the Finite Cell Method 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2021 Abstract In this work, the reliability of a residual-based error estimator for the Finite Cell method is established. The error estimator is suitable for the application of hp-adaptive finite elements and allows for Neumann boundary conditions on curved boundaries. The reliability proof of the error estimator relies on standard arguments of residual-based a posteriori error control, but includes several modifications with respect to the error contributions associated with the volume residuals as well as the jumps across inner edges and Neumann boundary parts. Important ingredients of the proof are Stein’s extension theorem and a modified trace theorem which estimates the norm of the trace on (curved) boundary parts in terms of the local mesh size and polynomial degree. The efficiency of the error estimator is also considered by discussing an artificial example which yields an efficiency index depending on the mesh-family parameter h. Numerical experiments on more realistic domains, however, suggest global efficiency with the occurrence of a large overestimation on only few cut elements. In the experiments the reliability of the error estimator is demonstrated for h- and p-uniform as well as for hp-geometric and h-adaptive refinements driven by the error estimator. The practical applicability of the error estimator is also studied for a 3D problem with a non-smooth solution. A posteriori error estimation Finite Cell method Residual-based hp-FEM Schröder, Andreas aut Enthalten in Journal of scientific computing Springer US, 1986 87(2021), 1 vom: 23. Feb. (DE-627)129217549 (DE-600)56055-8 (DE-576)065121945 0885-7474 nnns volume:87 year:2021 number:1 day:23 month:02 https://doi.org/10.1007/s10915-021-01417-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 87 2021 1 23 02 |
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10.1007/s10915-021-01417-y doi (DE-627)OLC2123934089 (DE-He213)s10915-021-01417-y-p DE-627 ger DE-627 rakwb eng 004 VZ 11 ssgn Di Stolfo, Paolo verfasserin (orcid)0000-0001-5735-5644 aut Reliable Residual-Based Error Estimation for the Finite Cell Method 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2021 Abstract In this work, the reliability of a residual-based error estimator for the Finite Cell method is established. The error estimator is suitable for the application of hp-adaptive finite elements and allows for Neumann boundary conditions on curved boundaries. The reliability proof of the error estimator relies on standard arguments of residual-based a posteriori error control, but includes several modifications with respect to the error contributions associated with the volume residuals as well as the jumps across inner edges and Neumann boundary parts. Important ingredients of the proof are Stein’s extension theorem and a modified trace theorem which estimates the norm of the trace on (curved) boundary parts in terms of the local mesh size and polynomial degree. The efficiency of the error estimator is also considered by discussing an artificial example which yields an efficiency index depending on the mesh-family parameter h. Numerical experiments on more realistic domains, however, suggest global efficiency with the occurrence of a large overestimation on only few cut elements. In the experiments the reliability of the error estimator is demonstrated for h- and p-uniform as well as for hp-geometric and h-adaptive refinements driven by the error estimator. The practical applicability of the error estimator is also studied for a 3D problem with a non-smooth solution. A posteriori error estimation Finite Cell method Residual-based hp-FEM Schröder, Andreas aut Enthalten in Journal of scientific computing Springer US, 1986 87(2021), 1 vom: 23. Feb. (DE-627)129217549 (DE-600)56055-8 (DE-576)065121945 0885-7474 nnns volume:87 year:2021 number:1 day:23 month:02 https://doi.org/10.1007/s10915-021-01417-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 87 2021 1 23 02 |
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10.1007/s10915-021-01417-y doi (DE-627)OLC2123934089 (DE-He213)s10915-021-01417-y-p DE-627 ger DE-627 rakwb eng 004 VZ 11 ssgn Di Stolfo, Paolo verfasserin (orcid)0000-0001-5735-5644 aut Reliable Residual-Based Error Estimation for the Finite Cell Method 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2021 Abstract In this work, the reliability of a residual-based error estimator for the Finite Cell method is established. The error estimator is suitable for the application of hp-adaptive finite elements and allows for Neumann boundary conditions on curved boundaries. The reliability proof of the error estimator relies on standard arguments of residual-based a posteriori error control, but includes several modifications with respect to the error contributions associated with the volume residuals as well as the jumps across inner edges and Neumann boundary parts. Important ingredients of the proof are Stein’s extension theorem and a modified trace theorem which estimates the norm of the trace on (curved) boundary parts in terms of the local mesh size and polynomial degree. The efficiency of the error estimator is also considered by discussing an artificial example which yields an efficiency index depending on the mesh-family parameter h. Numerical experiments on more realistic domains, however, suggest global efficiency with the occurrence of a large overestimation on only few cut elements. In the experiments the reliability of the error estimator is demonstrated for h- and p-uniform as well as for hp-geometric and h-adaptive refinements driven by the error estimator. The practical applicability of the error estimator is also studied for a 3D problem with a non-smooth solution. A posteriori error estimation Finite Cell method Residual-based hp-FEM Schröder, Andreas aut Enthalten in Journal of scientific computing Springer US, 1986 87(2021), 1 vom: 23. Feb. (DE-627)129217549 (DE-600)56055-8 (DE-576)065121945 0885-7474 nnns volume:87 year:2021 number:1 day:23 month:02 https://doi.org/10.1007/s10915-021-01417-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 87 2021 1 23 02 |
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10.1007/s10915-021-01417-y doi (DE-627)OLC2123934089 (DE-He213)s10915-021-01417-y-p DE-627 ger DE-627 rakwb eng 004 VZ 11 ssgn Di Stolfo, Paolo verfasserin (orcid)0000-0001-5735-5644 aut Reliable Residual-Based Error Estimation for the Finite Cell Method 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2021 Abstract In this work, the reliability of a residual-based error estimator for the Finite Cell method is established. The error estimator is suitable for the application of hp-adaptive finite elements and allows for Neumann boundary conditions on curved boundaries. The reliability proof of the error estimator relies on standard arguments of residual-based a posteriori error control, but includes several modifications with respect to the error contributions associated with the volume residuals as well as the jumps across inner edges and Neumann boundary parts. Important ingredients of the proof are Stein’s extension theorem and a modified trace theorem which estimates the norm of the trace on (curved) boundary parts in terms of the local mesh size and polynomial degree. The efficiency of the error estimator is also considered by discussing an artificial example which yields an efficiency index depending on the mesh-family parameter h. Numerical experiments on more realistic domains, however, suggest global efficiency with the occurrence of a large overestimation on only few cut elements. In the experiments the reliability of the error estimator is demonstrated for h- and p-uniform as well as for hp-geometric and h-adaptive refinements driven by the error estimator. The practical applicability of the error estimator is also studied for a 3D problem with a non-smooth solution. A posteriori error estimation Finite Cell method Residual-based hp-FEM Schröder, Andreas aut Enthalten in Journal of scientific computing Springer US, 1986 87(2021), 1 vom: 23. Feb. (DE-627)129217549 (DE-600)56055-8 (DE-576)065121945 0885-7474 nnns volume:87 year:2021 number:1 day:23 month:02 https://doi.org/10.1007/s10915-021-01417-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 87 2021 1 23 02 |
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Reliable Residual-Based Error Estimation for the Finite Cell Method |
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Abstract In this work, the reliability of a residual-based error estimator for the Finite Cell method is established. The error estimator is suitable for the application of hp-adaptive finite elements and allows for Neumann boundary conditions on curved boundaries. The reliability proof of the error estimator relies on standard arguments of residual-based a posteriori error control, but includes several modifications with respect to the error contributions associated with the volume residuals as well as the jumps across inner edges and Neumann boundary parts. Important ingredients of the proof are Stein’s extension theorem and a modified trace theorem which estimates the norm of the trace on (curved) boundary parts in terms of the local mesh size and polynomial degree. The efficiency of the error estimator is also considered by discussing an artificial example which yields an efficiency index depending on the mesh-family parameter h. Numerical experiments on more realistic domains, however, suggest global efficiency with the occurrence of a large overestimation on only few cut elements. In the experiments the reliability of the error estimator is demonstrated for h- and p-uniform as well as for hp-geometric and h-adaptive refinements driven by the error estimator. The practical applicability of the error estimator is also studied for a 3D problem with a non-smooth solution. © The Author(s) 2021 |
| abstractGer |
Abstract In this work, the reliability of a residual-based error estimator for the Finite Cell method is established. The error estimator is suitable for the application of hp-adaptive finite elements and allows for Neumann boundary conditions on curved boundaries. The reliability proof of the error estimator relies on standard arguments of residual-based a posteriori error control, but includes several modifications with respect to the error contributions associated with the volume residuals as well as the jumps across inner edges and Neumann boundary parts. Important ingredients of the proof are Stein’s extension theorem and a modified trace theorem which estimates the norm of the trace on (curved) boundary parts in terms of the local mesh size and polynomial degree. The efficiency of the error estimator is also considered by discussing an artificial example which yields an efficiency index depending on the mesh-family parameter h. Numerical experiments on more realistic domains, however, suggest global efficiency with the occurrence of a large overestimation on only few cut elements. In the experiments the reliability of the error estimator is demonstrated for h- and p-uniform as well as for hp-geometric and h-adaptive refinements driven by the error estimator. The practical applicability of the error estimator is also studied for a 3D problem with a non-smooth solution. © The Author(s) 2021 |
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Abstract In this work, the reliability of a residual-based error estimator for the Finite Cell method is established. The error estimator is suitable for the application of hp-adaptive finite elements and allows for Neumann boundary conditions on curved boundaries. The reliability proof of the error estimator relies on standard arguments of residual-based a posteriori error control, but includes several modifications with respect to the error contributions associated with the volume residuals as well as the jumps across inner edges and Neumann boundary parts. Important ingredients of the proof are Stein’s extension theorem and a modified trace theorem which estimates the norm of the trace on (curved) boundary parts in terms of the local mesh size and polynomial degree. The efficiency of the error estimator is also considered by discussing an artificial example which yields an efficiency index depending on the mesh-family parameter h. Numerical experiments on more realistic domains, however, suggest global efficiency with the occurrence of a large overestimation on only few cut elements. In the experiments the reliability of the error estimator is demonstrated for h- and p-uniform as well as for hp-geometric and h-adaptive refinements driven by the error estimator. The practical applicability of the error estimator is also studied for a 3D problem with a non-smooth solution. © The Author(s) 2021 |
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Reliable Residual-Based Error Estimation for the Finite Cell Method |
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Schröder, Andreas |
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