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arXiv · 1602.05354

An $hp$-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems

Mario Amrein·Jens M. Melenk·Thomas P. Wihler
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Abstract

In this paper we develop an $hp$-adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an $hp$-version adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully $hp$-adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples.

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Mario Amrein, Jens M. Melenk, Thomas P. Wihler. 2016-02-17. An $hp$-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems. https://doi.org/10.1002/mma.4113

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