Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 46, Issue 4, Pages 2039-2067Publisher
SIAM PUBLICATIONS
DOI: 10.1137/060674181
Keywords
reduced basis methods; a posteriori error estimation; Brezzi-Rappaz-Raviart theory; steady incompressible Navier-Stokes equations; natural convection
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This work focuses on the a posteriori error estimation for the reduced basis method applied to partial differential equations with quadratic nonlinearity and a. ne parameter dependence. We rely on natural norms-local parameter-dependent norms-to provide a sharp and computable lower bound of the inf-sup constant. We prove a formulation of the Brezzi-Rappaz-Raviart existence and uniqueness theorem in the presence of two distinct norms. This allows us to relax the existence condition and to sharpen the field variable error bound. We also provide a robust algorithm to compute the Sobolev embedding constants involved in the error bound and in the inf-sup lower bound computation. We apply our method to a steady natural convection problem in a closed cavity, with a Grashof number varying from 10 to 10(7).
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