Local parameter selection in the $C^0$ interior penalty method for the biharmonic equation
The symmetric $C^0$ interior penalty method is one of the most popular discontinuous Galerkin methods for the biharmonic equation. This paper introduces an automatic local selection of the involved stability parameter in terms of the geometry of the underlying triangulation for arbitrary polynomial...
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| creator | Bringmann, Philipp Carstensen, Carsten Streitberger, Julian |
| description | The symmetric $C^0$ interior penalty method is one of the most popular
discontinuous Galerkin methods for the biharmonic equation. This paper
introduces an automatic local selection of the involved stability parameter in
terms of the geometry of the underlying triangulation for arbitrary polynomial
degrees. The proposed choice ensures a stable discretization with guaranteed
discrete ellipticity constant. Numerical evidence for uniform and adaptive
mesh-refinement and various polynomial degrees supports the reliability and
efficiency of the local parameter selection and recommends this in practice.
The approach is documented in 2D for triangles, but the methodology behind can
be generalized to higher dimensions, to non-uniform polynomial degrees, and to
rectangular discretizations. Two appendices present the realization of our
proposed parameter selection in various established finite element software
packages as well as a detailed documentation of a self-contained MATLAB program
for the lowest-order $C^0$ interior penalty method. |
| doi_str_mv | 10.48550/arxiv.2209.05221 |
| format | Article |
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discontinuous Galerkin methods for the biharmonic equation. This paper
introduces an automatic local selection of the involved stability parameter in
terms of the geometry of the underlying triangulation for arbitrary polynomial
degrees. The proposed choice ensures a stable discretization with guaranteed
discrete ellipticity constant. Numerical evidence for uniform and adaptive
mesh-refinement and various polynomial degrees supports the reliability and
efficiency of the local parameter selection and recommends this in practice.
The approach is documented in 2D for triangles, but the methodology behind can
be generalized to higher dimensions, to non-uniform polynomial degrees, and to
rectangular discretizations. Two appendices present the realization of our
proposed parameter selection in various established finite element software
packages as well as a detailed documentation of a self-contained MATLAB program
for the lowest-order $C^0$ interior penalty method.</description><identifier>DOI: 10.48550/arxiv.2209.05221</identifier><language>eng</language><subject>Computer Science - Numerical Analysis ; Mathematics - Numerical Analysis</subject><creationdate>2022-09</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2209.05221$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2209.05221$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.1515/jnma-2023-0028$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Bringmann, Philipp</creatorcontrib><creatorcontrib>Carstensen, Carsten</creatorcontrib><creatorcontrib>Streitberger, Julian</creatorcontrib><title>Local parameter selection in the $C^0$ interior penalty method for the biharmonic equation</title><description>The symmetric $C^0$ interior penalty method is one of the most popular
discontinuous Galerkin methods for the biharmonic equation. This paper
introduces an automatic local selection of the involved stability parameter in
terms of the geometry of the underlying triangulation for arbitrary polynomial
degrees. The proposed choice ensures a stable discretization with guaranteed
discrete ellipticity constant. Numerical evidence for uniform and adaptive
mesh-refinement and various polynomial degrees supports the reliability and
efficiency of the local parameter selection and recommends this in practice.
The approach is documented in 2D for triangles, but the methodology behind can
be generalized to higher dimensions, to non-uniform polynomial degrees, and to
rectangular discretizations. Two appendices present the realization of our
proposed parameter selection in various established finite element software
packages as well as a detailed documentation of a self-contained MATLAB program
for the lowest-order $C^0$ interior penalty method.</description><subject>Computer Science - Numerical Analysis</subject><subject>Mathematics - Numerical Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotjztPwzAUhb0woMIPYMJD14Rrx07iEUW8pEhdOjEQXTvXiqW8cAOi_56kMB2dh470MXYnIFWl1vCA8Sd8p1KCSUFLKa7Zez057PmMEQdaKPIT9eSWMI08jHzpiO-rD9ivZi3DFPlMI_bLma_rbmq5X6NtZUOHcZjG4Dh9fuF2cMOuPPYnuv3XHTs-Px2r16Q-vLxVj3WCeSESI4RSLvPodd5qY60QUloBOWHROkQJRYaqxFIJb40wqgUiWxKQsaB0nu3Y_d_tBa6ZYxgwnpsNsrlAZr901Ez_</recordid><startdate>20220912</startdate><enddate>20220912</enddate><creator>Bringmann, Philipp</creator><creator>Carstensen, Carsten</creator><creator>Streitberger, Julian</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220912</creationdate><title>Local parameter selection in the $C^0$ interior penalty method for the biharmonic equation</title><author>Bringmann, Philipp ; Carstensen, Carsten ; Streitberger, Julian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a671-91144c3faf56d59bb1122b106ea7dcaa2073a48a841fb9194d0eeb8e0e9b04563</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Computer Science - Numerical Analysis</topic><topic>Mathematics - Numerical Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Bringmann, Philipp</creatorcontrib><creatorcontrib>Carstensen, Carsten</creatorcontrib><creatorcontrib>Streitberger, Julian</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bringmann, Philipp</au><au>Carstensen, Carsten</au><au>Streitberger, Julian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Local parameter selection in the $C^0$ interior penalty method for the biharmonic equation</atitle><date>2022-09-12</date><risdate>2022</risdate><abstract>The symmetric $C^0$ interior penalty method is one of the most popular
discontinuous Galerkin methods for the biharmonic equation. This paper
introduces an automatic local selection of the involved stability parameter in
terms of the geometry of the underlying triangulation for arbitrary polynomial
degrees. The proposed choice ensures a stable discretization with guaranteed
discrete ellipticity constant. Numerical evidence for uniform and adaptive
mesh-refinement and various polynomial degrees supports the reliability and
efficiency of the local parameter selection and recommends this in practice.
The approach is documented in 2D for triangles, but the methodology behind can
be generalized to higher dimensions, to non-uniform polynomial degrees, and to
rectangular discretizations. Two appendices present the realization of our
proposed parameter selection in various established finite element software
packages as well as a detailed documentation of a self-contained MATLAB program
for the lowest-order $C^0$ interior penalty method.</abstract><doi>10.48550/arxiv.2209.05221</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | Local parameter selection in the $C^0$ interior penalty method for the biharmonic equation |
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