Abstract
In this paper, we propose a certified reduced basis (RB) method for quasilinear parabolic problems with strongly monotone spatial differential operator. We provide a residual-based a posteriori error estimate for a space-time formulation and the corresponding efficiently computable bound for the certification of the method. We introduce a Petrov-Galerkin finite element discretization of the continuous space-time problem and use it as our reference in a posteriori error control. The Petrov-Galerkin discretization is further approximated by the Crank-Nicolson time-marching problem. It allows to use a POD-Greedy approach to construct the reduced-basis spaces of small dimensions and to apply the Empirical Interpolation Method (EIM) to guarantee the efficient offline-online computational procedure. In our approach, we compute the reduced basis solution in a time-marching framework while the RB approximation error in a space-time norm is controlled by our computable bound. Therefore, we combine a POD-Greedy approximation with a space-time Galerkin method.
Highlights
The certified reduced basis method is known as an efficient method for model order reduction of parametrized partial differential equations
We propose an L2(0, T ; V ) a posteriori error estimate, based on the spacetime variational formulation of quasilinear parabolic PDEs with strongly monotone differential operators
We consider a space-time variational formulation of quasilinear parabolic partial differential equations, which we denote as the exact problem
Summary
The certified reduced basis method is known as an efficient method for model order reduction of parametrized partial differential equations
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