Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes
In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equation...
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Springer Verlag
2017
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| Online Access: | https://eprints.nottingham.ac.uk/29674/ |
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| author | Antonietti, P. F. Houston, P. Hu, X. Sarti, M. Verani, M. |
| author_facet | Antonietti, P. F. Houston, P. Hu, X. Sarti, M. Verani, M. |
| author_sort | Antonietti, P. F. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polygonal/polyhedral meshes. We prove that the two-level method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p, provided that the number of smoothing steps, which depends on p, is chosen sufficiently large. An analogous result is obtained for the W-cycle multigrid algorithm, which is proved to be uniformly convergent with respect to the mesh size, the polynomial approximation degree, and the number of levels, provided the latter remains bounded and the number of smoothing steps is chosen sufficiently large. Numerical experiments are presented which underpin the theoretical predictions; moreover, the proposed multilevel solvers are shown to be convergent in practice, even when some of the theoretical assumptions are not fully satisfied. |
| first_indexed | 2025-11-14T19:06:30Z |
| format | Article |
| id | nottingham-29674 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:06:30Z |
| publishDate | 2017 |
| publisher | Springer Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-296742020-05-04T18:44:29Z https://eprints.nottingham.ac.uk/29674/ Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes Antonietti, P. F. Houston, P. Hu, X. Sarti, M. Verani, M. In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polygonal/polyhedral meshes. We prove that the two-level method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p, provided that the number of smoothing steps, which depends on p, is chosen sufficiently large. An analogous result is obtained for the W-cycle multigrid algorithm, which is proved to be uniformly convergent with respect to the mesh size, the polynomial approximation degree, and the number of levels, provided the latter remains bounded and the number of smoothing steps is chosen sufficiently large. Numerical experiments are presented which underpin the theoretical predictions; moreover, the proposed multilevel solvers are shown to be convergent in practice, even when some of the theoretical assumptions are not fully satisfied. Springer Verlag 2017-05-04 Article PeerReviewed Antonietti, P. F., Houston, P., Hu, X., Sarti, M. and Verani, M. (2017) Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes. Numerische Mathematik, 54 (4). pp. 1169-1198. ISSN 0029-599X hp-discontinuous Galerkin methods Polygonal/polyhedral grids Two-level and multigrid algorithms https://link.springer.com/article/10.1007/s10092-017-0223-6 doi:10.1007/s10092-017-0223-6 doi:10.1007/s10092-017-0223-6 |
| spellingShingle | hp-discontinuous Galerkin methods Polygonal/polyhedral grids Two-level and multigrid algorithms Antonietti, P. F. Houston, P. Hu, X. Sarti, M. Verani, M. Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes |
| title | Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes |
| title_full | Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes |
| title_fullStr | Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes |
| title_full_unstemmed | Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes |
| title_short | Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes |
| title_sort | multigrid algorithms for hp-version interior penalty discontinuous galerkin methods on polygonal and polyhedral meshes |
| topic | hp-discontinuous Galerkin methods Polygonal/polyhedral grids Two-level and multigrid algorithms |
| url | https://eprints.nottingham.ac.uk/29674/ https://eprints.nottingham.ac.uk/29674/ https://eprints.nottingham.ac.uk/29674/ |