An improved error bound for reduced basis approximation of linear parabolic problems
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], the inverse of which enters into error estimates: β[subscript...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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American Mathematical Society (AMS)
2015
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| Online Access: | http://hdl.handle.net/1721.1/97697 https://orcid.org/0000-0002-2631-6463 |
| _version_ | 1811077079790256128 |
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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], the inverse of which enters into error estimates: β[subscript δ] is unity for the heat equation; β[subscript δ] decreases 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. The paper contains a full analysis and various extensions for the formulation introduced briefly by Urban and Patera (2012) as well as numerical results for a model reaction-convection-diffusion equation. |
| first_indexed | 2024-09-23T10:37:34Z |
| format | Article |
| id | mit-1721.1/97697 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:37:34Z |
| publishDate | 2015 |
| publisher | American Mathematical Society (AMS) |
| record_format | dspace |
| spelling | mit-1721.1/976972022-10-24T05:27:47Z An improved error bound for reduced basis approximation of linear parabolic problems 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], the inverse of which enters into error estimates: β[subscript δ] is unity for the heat equation; β[subscript δ] decreases 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. The paper contains a full analysis and various extensions for the formulation introduced briefly by Urban and Patera (2012) as well as numerical results for a model reaction-convection-diffusion equation. 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) 2015-07-07T16:03:52Z 2015-07-07T16:03:52Z 2013-10 2012-12 Article http://purl.org/eprint/type/JournalArticle 0025-5718 1088-6842 http://hdl.handle.net/1721.1/97697 Urban, Karsten, and Anthony T. Patera. “An Improved Error Bound for Reduced Basis Approximation of Linear Parabolic Problems.” Mathematics of Computation 83, no. 288 (October 23, 2013): 1599–1615. © 2013 American Mathematical Society https://orcid.org/0000-0002-2631-6463 en_US http://dx.doi.org/10.1090/S0025-5718-2013-02782-2 Mathematics of Computation Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Mathematical Society (AMS) American Mathematical Society |
| spellingShingle | Urban, Karsten Patera, Anthony T. An improved error bound for reduced basis approximation of linear parabolic problems |
| title | An improved error bound for reduced basis approximation of linear parabolic problems |
| title_full | An improved error bound for reduced basis approximation of linear parabolic problems |
| title_fullStr | An improved error bound for reduced basis approximation of linear parabolic problems |
| title_full_unstemmed | An improved error bound for reduced basis approximation of linear parabolic problems |
| title_short | An improved error bound for reduced basis approximation of linear parabolic problems |
| title_sort | improved error bound for reduced basis approximation of linear parabolic problems |
| url | http://hdl.handle.net/1721.1/97697 https://orcid.org/0000-0002-2631-6463 |
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