An $hp$-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems
Numerical Analysis
2018-03-07 v1
Abstract
In this paper we develop an -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 -version adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully -adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples.
Keywords
Cite
@article{arxiv.1602.05354,
title = {An $hp$-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems},
author = {Mario Amrein and Jens M. Melenk and Thomas P. Wihler},
journal= {arXiv preprint arXiv:1602.05354},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1408.5221