A space-time certified reduced basis method for quasilinear parabolic partial differential equations

Abstract In this paper, we propose a certified reduced basis (RB) method for quasilinear parabolic problems with strongly monotone spatial differential operator. We provide residual-based posteriori error estimate space-time formulation and the corresponding efficiently computable bound certification of method. introduce Petrov-Galerkin finite element discretization continuous problem use it as our reference in control. The is further approximated by Crank-Nicolson time-marching problem. It allows to POD-Greedy approach construct reduced-basis spaces small dimensions apply Empirical Interpolation Method (EIM) guarantee efficient offline-online computational procedure. approach, compute solution framework while RB approximation norm controlled bound. Therefore, combine Galerkin