Improved a priori error estimates for a space-time finite element method for parabolic problems
Numerical Analysis
2025-03-13 v1 Numerical Analysis
Abstract
In this paper, we employ a space-time finite element method to discretize the parabolic initial-boundary value problem and extend its error analysis with refined estimates on unstructured space-time meshes. We establish higher-order estimates in three different norms, thereby supplementing existing research. Moreover, we obtain an optimal estimate in a norm stronger than that of the trial space. Finally, we present numerical examples to illustrate our theoretical results.
Cite
@article{arxiv.2503.09229,
title = {Improved a priori error estimates for a space-time finite element method for parabolic problems},
author = {Thi Thanh Mai Ta and Quang Huy Nguyen and Phi Hung Pham},
journal= {arXiv preprint arXiv:2503.09229},
year = {2025}
}