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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Format: | Article |
Language: | English |
Published: |
American Mathematical Society (AMS),
2015-07-07T16:03:52Z.
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Subjects: | |
Online Access: | Get fulltext |
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. 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) |
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