Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable continuous approximation to the solution on each mesh instance and...
| Authors: | ; ; ; |
|---|---|
| Format: | Article |
| Status: | Accepted version |
| Publication date: | 2021 |
| Country: | España |
| Institution: | Basque Center for Applied Mathematics (BCAM) |
| Repository: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1261 |
| Online Access: | http://hdl.handle.net/20.500.11824/1261 |
| Access Level: | Open access |
| Keyword: | goal-oriented adaptivity stabilized finite elements residual minimization inf-sup stability discontinuous Galerkin |
| _version_ | 1878741225800990720 |
|---|---|
| author | Rojas, S. |
| author2 | Pardo, D. Behnoudfare, P. Calo, V. M. |
| author2_role | author author author |
| author_browse | Behnoudfare, P. Calo, V. M. Pardo, D. Rojas, S. |
| author_facet | Rojas, S. Pardo, D. Behnoudfare, P. Calo, V. M. |
| author_role | author |
| collection | BIRD. BCAM's Institutional Repository Data |
| description | We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable continuous approximation to the solution on each mesh instance and a residual projection onto a broken polynomial space, which is a robust error estimator to minimize the discrete energy norm via automatic mesh refinement. In this work, we propose and analyze a goal-oriented adaptive algorithm for this stable residual minimization. We solve the primal and adjoint problems considering the same saddle-point formulation and different right-hand sides. By solving a third stable problem, we obtain two efficient error estimates to guide goal oriented adaptivity. We illustrate the performance of this goal-oriented adaptive strategy on advection-diffusion reaction problems. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_e1681a3eca584eb00a6d0f9e8bbc7cd1 |
| institution | Basque Center for Applied Mathematics (BCAM) |
| instname_str | Basque Center for Applied Mathematics (BCAM) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:bird.bcamath.org:20.500.11824/1261 |
| publishDate | 2021 |
| publishDateSort | 2021 |
| reponame_str | BIRD. BCAM's Institutional Repository Data |
| spelling | Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm Rojas, S. Pardo, D. Behnoudfare, P. Calo, V. M. goal-oriented adaptivity stabilized finite elements residual minimization inf-sup stability discontinuous Galerkin We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable continuous approximation to the solution on each mesh instance and a residual projection onto a broken polynomial space, which is a robust error estimator to minimize the discrete energy norm via automatic mesh refinement. In this work, we propose and analyze a goal-oriented adaptive algorithm for this stable residual minimization. We solve the primal and adjoint problems considering the same saddle-point formulation and different right-hand sides. By solving a third stable problem, we obtain two efficient error estimates to guide goal oriented adaptivity. We illustrate the performance of this goal-oriented adaptive strategy on advection-diffusion reaction problems. http://hdl.handle.net/20.500.11824/1261 |
| spellingShingle | Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm Rojas, S. goal-oriented adaptivity stabilized finite elements residual minimization inf-sup stability discontinuous Galerkin |
| status_str | acceptedVersion |
| title | Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm |
| title_full | Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm |
| title_fullStr | Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm |
| title_full_unstemmed | Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm |
| title_short | Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm |
| title_sort | Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm |
| topic | goal-oriented adaptivity stabilized finite elements residual minimization inf-sup stability discontinuous Galerkin |
| topic_facet | goal-oriented adaptivity stabilized finite elements residual minimization inf-sup stability discontinuous Galerkin |
| url | http://hdl.handle.net/20.500.11824/1261 |