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

Boris Vexler

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arXiv · 2411.06926

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

Boris Vexler

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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.

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Boris Vexler. 2024-11-11. A priori error estimates for finite element discretization of semilinear elliptic equations with non-Lipschitz nonlinearities. https://arxiv.org/abs/2411.06926

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