期刊
COMPTES RENDUS MATHEMATIQUE
卷 335, 期 3, 页码 289-294出版社
ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
DOI: 10.1016/S1631-073X(02)02466-4
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We consider Lagrangian reduced-basis methods for single-parameter symmetric coercive elliptic partial differential equations. We show that, for a logarithmic-(quasi-)uniform distribution of sample points, the reduced-basis approximation converges exponentially to the exact solution uniformly in parameter space. Furthermore, the convergence rate depends only weakly on the continuity-coercivity ratio of the operator: thus very low-dimensional approximations yield accurate solutions even for very wide parametric ranges. Numerical tests (reported elsewhere) corroborate the theoretical predictions.
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