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Fully Adaptive Newton-Galerkin Time Stepping Methods for Singularly Perturbed Parabolic Evolution Equations (1510.00622v1)
Published 2 Oct 2015 in math.NA
Abstract: In this paper we develop an adaptive procedure for the numerical solution of semilinear parabolic problems, with possible singular perturbations. Our approach combines a linearization technique using Newton's method with an adaptive discretization-which is based on a spatial finite element method and the backward Euler time stepping scheme-of the resulting sequence of linear problems. Upon deriving a robust a posteriori error analysis, we design a fully adaptive Newton-Galerkin time stepping algorithm. Numerical experiments underline the robustness and reliability of the proposed approach for various examples.