A priori error estimates for finite element discretization of semilinear elliptic equations with non-Lipschitz nonlinearities
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912113590534144 |
|---|---|
| author | Vexler, Boris |
| author_facet | Vexler, Boris |
| contents | 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-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06926 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A priori error estimates for finite element discretization of semilinear elliptic equations with non-Lipschitz nonlinearities Vexler, Boris Numerical Analysis 65N30, 65N15, 35J60, 35J65 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-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. |
| title | A priori error estimates for finite element discretization of semilinear elliptic equations with non-Lipschitz nonlinearities |
| topic | Numerical Analysis 65N30, 65N15, 35J60, 35J65 |
| url | https://arxiv.org/abs/2411.06926 |