An $hp$-Adaptive Newton-Discontinuous-Galerkin Finite Element Approach for Semilinear Elliptic Boundary Value Problems
Numerical Analysis
2016-07-25 v1
Abstract
In this paper we develop an -adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and an -version adaptive discontinuous Galerkin finite element discretisation, which, in turn, is based on a robust -version a posteriori residual analysis. Numerical experiments underline the robustness and reliability of the proposed approach for various examples.
Keywords
Cite
@article{arxiv.1607.06704,
title = {An $hp$-Adaptive Newton-Discontinuous-Galerkin Finite Element Approach for Semilinear Elliptic Boundary Value Problems},
author = {Paul Houston and Thomas P. Wihler},
journal= {arXiv preprint arXiv:1607.06704},
year = {2016}
}