| Issue |
ESAIM: M2AN
Volume 60, Number 1, January-February 2026
|
|
|---|---|---|
| Page(s) | 25 - 50 | |
| DOI | https://doi.org/10.1051/m2an/2025094 | |
| Published online | 30 January 2026 | |
Residual-based a posteriori error estimation for a space-time discontinuous Galerkin formulation of the Richards equation
1
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic
2
Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
27
January
2025
Accepted:
25
November
2025
In this article, we develop the a posteriori error analysis of a space-time discontinuous Galerkin finite element method for the Richards equation. Computable upper and lower bounds on the error in a residual dual norm are derived, which are explicit in the mesh size. Several numerical experiments demonstrate the performance of the a posteriori error bound within an mesh refinement algorithm, which refines the mesh as time evolves. Although this a posteriori error bound is on the residual dual norm, and is not a upper bound for the H1-norm, it is able to refine the areas of the mesh where the residual is large in a manner which reduces the H1-error and L1-error as well.
Mathematics Subject Classification: 65N15 / 65N30 / 65N50
Key words: Richards equation / a posteriori error estimates / space-time discontinuous Galerkin / adaptive refinement
© The authors. Published by EDP Sciences, SMAI 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.