Reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-Laplacian
We generalize the a posteriori techniques for the linear heat equation in [Ver03] to the case of the nonlinear parabolic p-Laplace problem thereby proving reliable and efficient a posteriori error estimates for a fully discrete implicite Euler Galerkin finite element scheme. The error is analyzed us...
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| Format: | Report |
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Springer
2011
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| _version_ | 1797052411027652608 |
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| author | Kreuzer, C |
| author_facet | Kreuzer, C |
| author_sort | Kreuzer, C |
| collection | OXFORD |
| description | We generalize the a posteriori techniques for the linear heat equation in [Ver03] to the case of the nonlinear parabolic p-Laplace problem thereby proving reliable and efficient a posteriori error estimates for a fully discrete implicite Euler Galerkin finite element scheme. The error is analyzed using the so-called quasi-norm and a related dual error expression. This leads to equivalence of the error and the residual, which is the key property for proving the error bounds. |
| first_indexed | 2024-03-06T18:31:14Z |
| format | Report |
| id | oxford-uuid:09b79855-4186-43f3-87a3-996ba792b8e5 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:31:14Z |
| publishDate | 2011 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:09b79855-4186-43f3-87a3-996ba792b8e52022-03-26T09:19:50ZReliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-LaplacianReporthttp://purl.org/coar/resource_type/c_93fcuuid:09b79855-4186-43f3-87a3-996ba792b8e5Mathematical Institute - ePrintsSpringer2011Kreuzer, CWe generalize the a posteriori techniques for the linear heat equation in [Ver03] to the case of the nonlinear parabolic p-Laplace problem thereby proving reliable and efficient a posteriori error estimates for a fully discrete implicite Euler Galerkin finite element scheme. The error is analyzed using the so-called quasi-norm and a related dual error expression. This leads to equivalence of the error and the residual, which is the key property for proving the error bounds. |
| spellingShingle | Kreuzer, C Reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-Laplacian |
| title | Reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-Laplacian |
| title_full | Reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-Laplacian |
| title_fullStr | Reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-Laplacian |
| title_full_unstemmed | Reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-Laplacian |
| title_short | Reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-Laplacian |
| title_sort | reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p laplacian |
| work_keys_str_mv | AT kreuzerc reliableandefficientaposteriorierrorestimatesforfiniteelementapproximationsoftheparabolicplaplacian |