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 |
Published: |
Elsevier
2015
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Online Access: | http://hdl.handle.net/1721.1/99384 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]: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. |
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