Work

A priori error estimates for finite element discretization of semilinear elliptic equations with non-Lipschitz nonlinearities

Year: 2025

Type: article

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 non-decreasing including the case of non-Lipschitz or even non-Hölder 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.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2025019

Author: Boris Vexler

Institution: Technical University of Munich

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

OpenAlex ID: W4408697250