Variational Convergence of IP-DGFEM
In this paper, we develop the theory required to perform a variational convergence analysis for discontinuous Galerkin nite element methods when applied to minimization problems. For Sobolev indices in $\left[1;\infty\right)$, we prove generalizations of many techniques of classical analysis in Sobo...
| Main Authors: | , |
|---|---|
| Format: | Report |
| Published: |
Unspecified
2007
|
| _version_ | 1826266001059086336 |
|---|---|
| author | Buffa, A Ortner, C |
| author_facet | Buffa, A Ortner, C |
| author_sort | Buffa, A |
| collection | OXFORD |
| description | In this paper, we develop the theory required to perform a variational convergence analysis for discontinuous Galerkin nite element methods when applied to minimization problems. For Sobolev indices in $\left[1;\infty\right)$, we prove generalizations of many techniques of classical analysis in Sobolev spaces and apply them to a typical energy minimization problem for which we prove convergence of a variational interior penalty discontinuous Galerkin nite element method (VIPDGFEM). Our main tool in this analysis is a theorem which allows the extraction of a "weakly" converging subsequence of a family of discrete solutions and which shows that any "weak limit" is a Sobolev function. |
| first_indexed | 2024-03-06T20:32:21Z |
| format | Report |
| id | oxford-uuid:31789373-b5ec-4033-9ed4-59ad4a939c2f |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:32:21Z |
| publishDate | 2007 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:31789373-b5ec-4033-9ed4-59ad4a939c2f2022-03-26T13:08:13ZVariational Convergence of IP-DGFEMReporthttp://purl.org/coar/resource_type/c_93fcuuid:31789373-b5ec-4033-9ed4-59ad4a939c2fMathematical Institute - ePrintsUnspecified2007Buffa, AOrtner, CIn this paper, we develop the theory required to perform a variational convergence analysis for discontinuous Galerkin nite element methods when applied to minimization problems. For Sobolev indices in $\left[1;\infty\right)$, we prove generalizations of many techniques of classical analysis in Sobolev spaces and apply them to a typical energy minimization problem for which we prove convergence of a variational interior penalty discontinuous Galerkin nite element method (VIPDGFEM). Our main tool in this analysis is a theorem which allows the extraction of a "weakly" converging subsequence of a family of discrete solutions and which shows that any "weak limit" is a Sobolev function. |
| spellingShingle | Buffa, A Ortner, C Variational Convergence of IP-DGFEM |
| title | Variational Convergence of IP-DGFEM |
| title_full | Variational Convergence of IP-DGFEM |
| title_fullStr | Variational Convergence of IP-DGFEM |
| title_full_unstemmed | Variational Convergence of IP-DGFEM |
| title_short | Variational Convergence of IP-DGFEM |
| title_sort | variational convergence of ip dgfem |
| work_keys_str_mv | AT buffaa variationalconvergenceofipdgfem AT ortnerc variationalconvergenceofipdgfem |