Time and space adaptivity for the second-order wave equation
The aim of this paper is to show that, for a linear second-order hyperbolic equation discretized by the backward Euler scheme in time and continuous piecewise linear finite elements in space, the adaptation of the time steps can be combined with spatial mesh adaptivity in an optimal way. We derive a...
| Main Authors: | , |
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| Format: | Report |
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Unspecified
2004
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| _version_ | 1826281071072772096 |
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| author | Bernardi, C Suli, E |
| author_facet | Bernardi, C Suli, E |
| author_sort | Bernardi, C |
| collection | OXFORD |
| description | The aim of this paper is to show that, for a linear second-order hyperbolic equation discretized by the backward Euler scheme in time and continuous piecewise linear finite elements in space, the adaptation of the time steps can be combined with spatial mesh adaptivity in an optimal way. We derive a priori and a posteriori error estimates which admit, as much as it is possible, the decoupling of the errors committed in the temporal and spatial discretizations. |
| first_indexed | 2024-03-07T00:23:16Z |
| format | Report |
| id | oxford-uuid:7d433035-a8de-4a84-8cc4-a64e8c83eae0 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:23:16Z |
| publishDate | 2004 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:7d433035-a8de-4a84-8cc4-a64e8c83eae02022-03-26T21:02:27ZTime and space adaptivity for the second-order wave equationReporthttp://purl.org/coar/resource_type/c_93fcuuid:7d433035-a8de-4a84-8cc4-a64e8c83eae0Mathematical Institute - ePrintsUnspecified2004Bernardi, CSuli, EThe aim of this paper is to show that, for a linear second-order hyperbolic equation discretized by the backward Euler scheme in time and continuous piecewise linear finite elements in space, the adaptation of the time steps can be combined with spatial mesh adaptivity in an optimal way. We derive a priori and a posteriori error estimates which admit, as much as it is possible, the decoupling of the errors committed in the temporal and spatial discretizations. |
| spellingShingle | Bernardi, C Suli, E Time and space adaptivity for the second-order wave equation |
| title | Time and space adaptivity for the second-order wave equation |
| title_full | Time and space adaptivity for the second-order wave equation |
| title_fullStr | Time and space adaptivity for the second-order wave equation |
| title_full_unstemmed | Time and space adaptivity for the second-order wave equation |
| title_short | Time and space adaptivity for the second-order wave equation |
| title_sort | time and space adaptivity for the second order wave equation |
| work_keys_str_mv | AT bernardic timeandspaceadaptivityforthesecondorderwaveequation AT sulie timeandspaceadaptivityforthesecondorderwaveequation |