Fully Adaptive Newton-Galerkin Methods for Semilinear Elliptic Partial Differential Equations

2014/08/22 by Amrein, Mario, Wihler, Thomas P. · 1 citation
#49M15 #58C15 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1408.5221

Abstract

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for different examples.

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• Newton's method in adaptive iteratively linearized FEM

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