| Issue |
ESAIM: M2AN
Volume 59, Number 6, November-December 2025
|
|
|---|---|---|
| Page(s) | 3363 - 3383 | |
| DOI | https://doi.org/10.1051/m2an/2025093 | |
| Published online | 17 December 2025 | |
Optimal finite element approximations of monotone semilinear elliptic pde with subcritical nonlinearities
Mathematics Institute, University of Bern, CH-3012 Bern, Switzerland
* Corresponding author: thomas.wihler@unibe.ch
Received:
15
April
2025
Accepted:
24
October
2025
We study iterative finite element approximations for the numerical approximation of semilinear elliptic boundary value problems with monotone nonlinear reactions of subcritical growth. The focus of our contribution is on an optimal a priori error estimate for a contractive Picard type iteration scheme on meshes that are locally refined towards possible corner singularities in polygonal domains. Our analysis involves, in particular, an elliptic regularity result in weighted Sobolev spaces and the use of the Trudinger inequality, which is instrumental in dealing with subcritically growing nonlinearities. A series of numerical experiments confirm the accuracy and efficiency of our method.
Mathematics Subject Classification: 47J25 / 65J15 / 65N30
Key words: Semilinear elliptic boundary value problems / monotone operators / subcritical growth / corner-weighted Sobolev spaces / elliptic corner singularities / finite element methods / optimal convergence / graded meshes in polygons / Trudinger inequality
© The authors. Published by EDP Sciences, SMAI 2025
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