A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics
We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous P^3_{k}-P_{k-1} elements whereas the magnetic part of the equations is app...
| Main Authors: | , , |
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| Format: | Article |
| Published: |
Springer
2008
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| Online Access: | https://eprints.nottingham.ac.uk/912/ |
| _version_ | 1848790500842143744 |
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| author | Houston, Paul Schoetzau, Dominik Wei, Xiaoxi |
| author_facet | Houston, Paul Schoetzau, Dominik Wei, Xiaoxi |
| author_sort | Houston, Paul |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous P^3_{k}-P_{k-1} elements whereas the magnetic part of the equations is approximated by discontinuous P^3_{k}-P_{k+1} elements. We carry out a complete a-priori error analysis and prove that the energy norm error is convergent of order O(h^k) in the mesh size h. We also show that the method is able to correctly capture and resolve the strongest magnetic singularities in non-convex polyhedral domains. These results are verified in a series of numerical experiments. |
| first_indexed | 2025-11-14T18:13:37Z |
| format | Article |
| id | nottingham-912 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:13:37Z |
| publishDate | 2008 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-9122020-05-04T20:27:46Z https://eprints.nottingham.ac.uk/912/ A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics Houston, Paul Schoetzau, Dominik Wei, Xiaoxi We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous P^3_{k}-P_{k-1} elements whereas the magnetic part of the equations is approximated by discontinuous P^3_{k}-P_{k+1} elements. We carry out a complete a-priori error analysis and prove that the energy norm error is convergent of order O(h^k) in the mesh size h. We also show that the method is able to correctly capture and resolve the strongest magnetic singularities in non-convex polyhedral domains. These results are verified in a series of numerical experiments. Springer 2008 Article NonPeerReviewed Houston, Paul, Schoetzau, Dominik and Wei, Xiaoxi (2008) A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics. Journal of Scientific Computing . (Submitted) |
| spellingShingle | Houston, Paul Schoetzau, Dominik Wei, Xiaoxi A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics |
| title | A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics |
| title_full | A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics |
| title_fullStr | A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics |
| title_full_unstemmed | A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics |
| title_short | A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics |
| title_sort | mixed discontinuous galerkin method for incompressible magnetohydrodynamics |
| url | https://eprints.nottingham.ac.uk/912/ |