A space-time finite element method for parabolic obstacle problems
Numerical Analysis
2025-03-12 v1 Numerical Analysis
Abstract
We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on simplicial and prismatic meshes are studied and we show a priori error estimates for both. Convergence rates are derived for sufficiently smooth solutions. Reliable a posteriori bounds are provided and used to steer an adaptive algorithm. Numerical experiments including a one-phase Stefan problem and an American option pricing problem are presented.
Cite
@article{arxiv.2503.07808,
title = {A space-time finite element method for parabolic obstacle problems},
author = {José Joaquín Carvajal and Davood Damircheli and Thomas Führer and Francisco Fuica and Michael Karkulik},
journal= {arXiv preprint arXiv:2503.07808},
year = {2025}
}