English

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 hphp-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 hphp-version adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully hphp-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