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Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations

Abstract : 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 preditions.
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Submitted on : Monday, March 11, 2013 - 12:42:18 PM
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Yvon Maday, Anthony T. Patera, Gabriel Turinici. Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2002, 335 (3), pp.289-294. ⟨10.1016/S1631-073X(02)02466-4⟩. ⟨hal-00798389⟩

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