hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization.
We consider a family of hp-version discontinuous Galerkin finite element methods with least-squares stabilization for symmetric systems of first-order partial differential equations. The family includes the classical discontinuous Galerkin finite element method, with and without streamline-diffusion...
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| Format: | Journal article |
| Language: | English |
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2002
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| _version_ | 1797063887555657728 |
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| author | Houston, P Jensen, M Süli, E |
| author_facet | Houston, P Jensen, M Süli, E |
| author_sort | Houston, P |
| collection | OXFORD |
| description | We consider a family of hp-version discontinuous Galerkin finite element methods with least-squares stabilization for symmetric systems of first-order partial differential equations. The family includes the classical discontinuous Galerkin finite element method, with and without streamline-diffusion stabilization, as well as the discontinuous version of the Galerkin least-squares finite element method. An hp-optimal error bound is derived in the associated DG-norm. If the solution of the problem is elementwise analytic, an exponential rate of convergence under p-refinement is proved. We perform numerical experiments both to illustrate the theoretical results and to compare the various methods within the family. |
| first_indexed | 2024-03-06T21:06:23Z |
| format | Journal article |
| id | oxford-uuid:3c9c73ba-9e6a-4df1-a539-3030902e4508 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:06:23Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:3c9c73ba-9e6a-4df1-a539-3030902e45082022-03-26T14:14:37Zhp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3c9c73ba-9e6a-4df1-a539-3030902e4508EnglishSymplectic Elements at Oxford2002Houston, PJensen, MSüli, EWe consider a family of hp-version discontinuous Galerkin finite element methods with least-squares stabilization for symmetric systems of first-order partial differential equations. The family includes the classical discontinuous Galerkin finite element method, with and without streamline-diffusion stabilization, as well as the discontinuous version of the Galerkin least-squares finite element method. An hp-optimal error bound is derived in the associated DG-norm. If the solution of the problem is elementwise analytic, an exponential rate of convergence under p-refinement is proved. We perform numerical experiments both to illustrate the theoretical results and to compare the various methods within the family. |
| spellingShingle | Houston, P Jensen, M Süli, E hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization. |
| title | hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization. |
| title_full | hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization. |
| title_fullStr | hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization. |
| title_full_unstemmed | hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization. |
| title_short | hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization. |
| title_sort | hp discontinuous galerkin finite element methods with least squares stabilization |
| work_keys_str_mv | AT houstonp hpdiscontinuousgalerkinfiniteelementmethodswithleastsquaresstabilization AT jensenm hpdiscontinuousgalerkinfiniteelementmethodswithleastsquaresstabilization AT sulie hpdiscontinuousgalerkinfiniteelementmethodswithleastsquaresstabilization |