Work

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: Springer Link (Chiba Institute of Technology)

DOI: 10.1051/m2an/2025019/pdf

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: green

OpenAlex ID: W6959646194

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