Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations. (English. Abridged French version) Zbl 1009.65066
Summary: 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.
MSC:
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
Keywords:
finite element method; Lagrangian reduced-basis methods; symmetric coercive elliptic partial differential equations; convergenceReferences:
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