Reduced-basis approximation of the viscous Burgers equation: rigorous a posteriori error bounds

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 Brezzi, Rappaz and Raviart (Numer. Math. 36 (1980) 1–25) framework 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.