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 |
| Published: |
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 |
| Summary: | 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. |
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