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Titre : |
Improved Successive Constraint Method Based A Posteriori Error Estimate for Reduced Basis Approximation of 2D Maxwells Problem |
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Année : |
2009 |
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Type : |
article (revue avec comité de lecture) |
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Auteurs : |
Y. Chen, J. Hesthaven, Y. Maday, J. Rodríguez |
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Résumé : |
In a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equa-
tions, the construction of lower bounds for the coercivity and inf-sup stability constants is essential. In [7], the
authors presented an efficient method, compatible with an off-line/on-line strategy, where the on-line computation
is reduced to minimizing a linear functional under a few linear constraints. These constraints depend on nested
sets of parameters obtained iteratively using a greedy algorithm. We improve here this method so that it becomes
more efficient due to a nice property, namely, that the computed lower bound is monotonically increasing with
respect to the size of the nested sets. This improved evaluation of the inf-sup constant is then used to consider
a reduced basis approximation of a parameter dependent electromagnetic cavity problem both for the greedy
construction of the elements of the basis and the subsequent validation of the reduced basis approximation. The
problem we consider has resonance features for some choices of the parameters that are well captured by the
methodology. |
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Thèmes : |
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Référence : |
ESAIM: Mathematical Modelling and Numerical Analysis - vol. 43(6) (pp 1099--1116 ) |
