| Issue |
ESAIM: M2AN
Volume 59, Number 2, March-April 2025
|
|
|---|---|---|
| Page(s) | 1095 - 1112 | |
| DOI | https://doi.org/10.1051/m2an/2025019 | |
| Published online | 08 April 2025 | |
A priori error estimates for finite element discretization of semilinear elliptic equations with non-Lipschitz nonlinearities
Technical University of Munich, School of Computation, Information and Technology, Department of Mathematics, Garching, Germany
* Corresponding author: vexler@tum.de
Received:
27
November
2024
Accepted:
19
March
2025
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.
Mathematics Subject Classification: 65N30 / 65N15 / 35J60 / 35J65
Key words: Semilinear equation / non-Lipschiz nonlinearity / finite elements / error estimates
© The authors. Published by EDP Sciences, SMAI 2025
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