A posteriori error analysis for stabilised finite element approximations of transport problems
We develop the a posteriori error analysis of stabilised finite element approximations to linear transport problems via duality arguments. Two alternative dual problems are considered: one is based on the formal adjoint of the hyperbolic differential operator, the other on the transposition of the b...
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| Format: | Report |
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Unspecified
1999
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| _version_ | 1797053900764741632 |
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| author | Houston, P Rannacher, R Suli, E |
| author_facet | Houston, P Rannacher, R Suli, E |
| author_sort | Houston, P |
| collection | OXFORD |
| description | We develop the a posteriori error analysis of stabilised finite element approximations to linear transport problems via duality arguments. Two alternative dual problems are considered: one is based on the formal adjoint of the hyperbolic differential operator, the other on the transposition of the bilinear form for the stabilised finite element method. We show both analytically and through numerical experiments that the second approach is superior in the sense that it leads to sharper a posteriori error bounds and more economical adaptively refined meshes. |
| first_indexed | 2024-03-06T18:50:02Z |
| format | Report |
| id | oxford-uuid:0fe9585d-3580-4df3-8328-1d454c0b5a9a |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:50:02Z |
| publishDate | 1999 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:0fe9585d-3580-4df3-8328-1d454c0b5a9a2022-03-26T09:53:38ZA posteriori error analysis for stabilised finite element approximations of transport problemsReporthttp://purl.org/coar/resource_type/c_93fcuuid:0fe9585d-3580-4df3-8328-1d454c0b5a9aMathematical Institute - ePrintsUnspecified1999Houston, PRannacher, RSuli, EWe develop the a posteriori error analysis of stabilised finite element approximations to linear transport problems via duality arguments. Two alternative dual problems are considered: one is based on the formal adjoint of the hyperbolic differential operator, the other on the transposition of the bilinear form for the stabilised finite element method. We show both analytically and through numerical experiments that the second approach is superior in the sense that it leads to sharper a posteriori error bounds and more economical adaptively refined meshes. |
| spellingShingle | Houston, P Rannacher, R Suli, E A posteriori error analysis for stabilised finite element approximations of transport problems |
| title | A posteriori error analysis for stabilised finite element approximations of transport problems |
| title_full | A posteriori error analysis for stabilised finite element approximations of transport problems |
| title_fullStr | A posteriori error analysis for stabilised finite element approximations of transport problems |
| title_full_unstemmed | A posteriori error analysis for stabilised finite element approximations of transport problems |
| title_short | A posteriori error analysis for stabilised finite element approximations of transport problems |
| title_sort | posteriori error analysis for stabilised finite element approximations of transport problems |
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