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

Amrein, Mario; Wihler, Thomas (2015). Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations. SIAM Journal on Scientific Computing, 37(4), A1637-A1657. Society for Industrial and Applied Mathematics 10.1137/140983537

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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 prediction-type adaptive Newton methods and a linear 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 various examples

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