Fully Adaptive Newton-Galerkin Methods for Semilinear Elliptic Partial Differential Equations
Numerical Analysis
2014-08-27 v2
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.
Cite
@article{arxiv.1408.5221,
title = {Fully Adaptive Newton-Galerkin Methods for Semilinear Elliptic Partial Differential Equations},
author = {Mario Amrein and Thomas P. Wihler},
journal= {arXiv preprint arXiv:1408.5221},
year = {2014}
}