A priori error estimates for finite element discretization of semilinear elliptic equations with non-Lipschitz nonlinearities
Numerical Analysis
2024-11-12 v1 Numerical Analysis
Abstract
In this paper we develop numerical analysis for finite element discretization of semilinear elliptic equations with potentially non-Lipschitz nonlinearites. The nonlinearity is essecially assumed to be continuous and monotonically decreasing including the case of non-Lipschitz or even non-H\"older continuous nonlinearities. For a direct discretization (without any regularization) with linear finite elements we derive error estimates with respect to various norms and illustrate these results with a numerical example.
Cite
@article{arxiv.2411.06926,
title = {A priori error estimates for finite element discretization of semilinear elliptic equations with non-Lipschitz nonlinearities},
author = {Boris Vexler},
journal= {arXiv preprint arXiv:2411.06926},
year = {2024}
}