A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems
We consider a variant of the hp-version interior penalty discontinuous Galerkin finite element method (IP-DGFEM) for second order problems of degenerate type. We do not assume uniform ellipticity of the diffusion tensor. Moreover, diffusion tensors or arbitrary form are covered in the theory present...
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| Format: | Report |
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Unspecified
2005
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| _version_ | 1797082573234503680 |
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| author | Georgoulis, E Lasis, A |
| author_facet | Georgoulis, E Lasis, A |
| author_sort | Georgoulis, E |
| collection | OXFORD |
| description | We consider a variant of the hp-version interior penalty discontinuous Galerkin finite element method (IP-DGFEM) for second order problems of degenerate type. We do not assume uniform ellipticity of the diffusion tensor. Moreover, diffusion tensors or arbitrary form are covered in the theory presented. A new, refined recipe for the choice of the discontinuity-penalisation parameter (that is present in the formlation of the IP-DGFEM) is given. Making use of the recently introduced augmented Sobolev space framework, we prove an hp-optimal error bound in the energy norm and an h-optimal and slightly p-suboptimal (by only half an order of p) bound in the L2 norm, provided that the solution belongs to an augmented Sobolev space. |
| first_indexed | 2024-03-07T01:29:50Z |
| format | Report |
| id | oxford-uuid:933a15ac-a4a8-4c2b-98c8-a6b05e6593bb |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:29:50Z |
| publishDate | 2005 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:933a15ac-a4a8-4c2b-98c8-a6b05e6593bb2022-03-26T23:30:50ZA note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problemsReporthttp://purl.org/coar/resource_type/c_93fcuuid:933a15ac-a4a8-4c2b-98c8-a6b05e6593bbMathematical Institute - ePrintsUnspecified2005Georgoulis, ELasis, AWe consider a variant of the hp-version interior penalty discontinuous Galerkin finite element method (IP-DGFEM) for second order problems of degenerate type. We do not assume uniform ellipticity of the diffusion tensor. Moreover, diffusion tensors or arbitrary form are covered in the theory presented. A new, refined recipe for the choice of the discontinuity-penalisation parameter (that is present in the formlation of the IP-DGFEM) is given. Making use of the recently introduced augmented Sobolev space framework, we prove an hp-optimal error bound in the energy norm and an h-optimal and slightly p-suboptimal (by only half an order of p) bound in the L2 norm, provided that the solution belongs to an augmented Sobolev space. |
| spellingShingle | Georgoulis, E Lasis, A A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems |
| title | A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems |
| title_full | A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems |
| title_fullStr | A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems |
| title_full_unstemmed | A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems |
| title_short | A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems |
| title_sort | note on the design of hp version interior penalty discontinuous galerkin finite element methods for degenerate problems |
| work_keys_str_mv | AT georgoulise anoteonthedesignofhpversioninteriorpenaltydiscontinuousgalerkinfiniteelementmethodsfordegenerateproblems AT lasisa anoteonthedesignofhpversioninteriorpenaltydiscontinuousgalerkinfiniteelementmethodsfordegenerateproblems AT georgoulise noteonthedesignofhpversioninteriorpenaltydiscontinuousgalerkinfiniteelementmethodsfordegenerateproblems AT lasisa noteonthedesignofhpversioninteriorpenaltydiscontinuousgalerkinfiniteelementmethodsfordegenerateproblems |