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A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. (English) Zbl 1079.65096
The authors extend the earlier developed reduced-basis methods for elliptic equations to the case of parabolic equations treating the time as additional parameter. First, the authors discuss the reduced-basis approximation. Then rigorous and sharp a posteriori error bounds are considered and an optimal procedure to select the optimal selecting set is proposed. Finally, adequate numerical results are presented.

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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