A new error bound for reduced basis approximation of parabolic partial differential equations
We consider a space–time variational formulation for linear parabolic partial differential equations. We introduce an associated Petrov–Galerkin truth finite element discretization with favorable discrete inf-sup constant β[subscript δ]:β[subscript δ] is unity for the heat equation; β[subscript δ] g...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Elsevier
2015
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| Online Access: | http://hdl.handle.net/1721.1/99384 https://orcid.org/0000-0002-2631-6463 |
| _version_ | 1826206662749323264 |
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| author | Urban, Karsten Patera, Anthony T. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Urban, Karsten Patera, Anthony T. |
| author_sort | Urban, Karsten |
| collection | MIT |
| description | We consider a space–time variational formulation for linear parabolic partial differential equations. We introduce an associated Petrov–Galerkin truth finite element discretization with favorable discrete inf-sup constant β[subscript δ]:β[subscript δ] is unity for the heat equation; β[subscript δ] grows only linearly in time for non-coercive (but asymptotically stable) convection operators. The latter in turn permits effective long-time a posteriori error bounds for reduced basis approximations, in sharp contrast to classical (pessimistic) exponentially growing energy estimates. |
| first_indexed | 2024-09-23T13:36:37Z |
| format | Article |
| id | mit-1721.1/99384 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:36:37Z |
| publishDate | 2015 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/993842022-10-01T16:00:37Z A new error bound for reduced basis approximation of parabolic partial differential equations Urban, Karsten Patera, Anthony T. Massachusetts Institute of Technology. Department of Mechanical Engineering Patera, Anthony T. We consider a space–time variational formulation for linear parabolic partial differential equations. We introduce an associated Petrov–Galerkin truth finite element discretization with favorable discrete inf-sup constant β[subscript δ]:β[subscript δ] is unity for the heat equation; β[subscript δ] grows only linearly in time for non-coercive (but asymptotically stable) convection operators. The latter in turn permits effective long-time a posteriori error bounds for reduced basis approximations, in sharp contrast to classical (pessimistic) exponentially growing energy estimates. United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-09-1-0613) United States. Office of Naval Research (Grant N00014-11-1-0713) 2015-10-21T14:42:49Z 2015-10-21T14:42:49Z 2012-02 2012-01 Article http://purl.org/eprint/type/JournalArticle 1631073X http://hdl.handle.net/1721.1/99384 Urban, Karsten, and Anthony T. Patera. “A New Error Bound for Reduced Basis Approximation of Parabolic Partial Differential Equations.” Comptes Rendus Mathematique 350, no. 3–4 (February 2012): 203–207. https://orcid.org/0000-0002-2631-6463 en_US http://dx.doi.org/10.1016/j.crma.2012.01.026 Comptes Rendus Mathematique Creative Commons Attribution-Noncommercial-NoDerivatives http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier MIT Web Domain |
| spellingShingle | Urban, Karsten Patera, Anthony T. A new error bound for reduced basis approximation of parabolic partial differential equations |
| title | A new error bound for reduced basis approximation of parabolic partial differential equations |
| title_full | A new error bound for reduced basis approximation of parabolic partial differential equations |
| title_fullStr | A new error bound for reduced basis approximation of parabolic partial differential equations |
| title_full_unstemmed | A new error bound for reduced basis approximation of parabolic partial differential equations |
| title_short | A new error bound for reduced basis approximation of parabolic partial differential equations |
| title_sort | new error bound for reduced basis approximation of parabolic partial differential equations |
| url | http://hdl.handle.net/1721.1/99384 https://orcid.org/0000-0002-2631-6463 |
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