Computational Methods in Applied Mathematics
Editor-in-Chief: Carstensen, Carsten
Managing Editor: Matus, Piotr
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IMPACT FACTOR 2016: 1.097
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Source Normalized Impact per Paper (SNIP) 2016: 0.887
Mathematical Citation Quotient (MCQ) 2016: 0.75
Goal-Oriented Error Estimation for the Fractional Step Theta Scheme
In this work, we derive a goal-oriented a posteriori error estimator for the error due to time-discretization of nonlinear parabolic partial differential equations by the fractional step theta method. This time-stepping scheme is assembled by three steps of the general theta method, that also unifies simple schemes like forward and backward Euler as well as the Crank–Nicolson method. Further, by combining three substeps of the theta time-stepping scheme, the fractional step theta time-stepping scheme is derived. It possesses highly desired stability and numerical dissipation properties and is second order accurate. The derived error estimator is based on a Petrov–Galerkin formulation that is up to a numerical quadrature error equivalent to the theta time-stepping scheme. The error estimator is assembled as one weighted residual term given by the dual weighted residual method and one additional residual estimating the Galerkin error between time-stepping scheme and Petrov–Galerkin formulation.
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