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Reduced-basis approximation of the viscous Burgers equation: Rigorous a posteriori error bounds. (English. Abridged French version) Zbl 1036.65075

Summary: We present rigorous, sharp, and inexpensive a posteriori error bounds for reduced-basis approximations of the viscosity-parametrized Burgers equation. There are two critical ingredients: the framework of F. Brezzi, J. Rappaz and P. A. Raviart [Numer. Math. 36, 1–25 (1980; Zbl 0488.65021)] for analysis of approximations of nonlinear elliptic partial differential equations; and offline/online computational procedures for efficient calculation of the necessary continuity and stability constants, and of the dual norm of the residual. Numerical results confirm the performance of the error bounds.

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
35Q53 KdV equations (Korteweg-de Vries equations)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

Citations:

Zbl 0488.65021
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References:

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