Adaptive finite elements for obstacle problems
Numerical Analysis
2026-01-28 v2 Numerical Analysis
Abstract
We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed computational meshes for any inequality-constrained problem because the coincidence set has an unknown shape. Consequently, we demonstrate how -adaptivity can be used to resolve the unknown coincidence set. We demonstrate some practical challenges that must be overcome in the application of the adaptive method.
Cite
@article{arxiv.2410.22991,
title = {Adaptive finite elements for obstacle problems},
author = {Tom Gustafsson},
journal= {arXiv preprint arXiv:2410.22991},
year = {2026}
}
Comments
A misleading explanation of the "diffusion parameter" was corrected in revision v2