| Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
|---|---|---|
| Page(s) | 2131 - 2158 | |
| DOI | https://doi.org/10.1051/m2an/2023035 | |
| Published online | 03 July 2023 | |
Error estimates for a finite volume scheme for advection–diffusion equations with rough coefficients
Institut für Analysis und Numerik, Westfälische Wilhelms-Universität Münster, Orléans-Ring 10, 48149 Münster, Germany
* Corresponding author: a.schlichting@uni-muenster.de
Received:
4
October
2022
Accepted:
23
April
2023
We study the implicit upwind finite volume scheme for numerically approximating the advection–diffusion equation with a vector field in the low regularity DiPerna–Lions setting. That is, we are concerned with advecting velocity fields that are spatially Sobolev regular and data that are merely integrable. We prove that on unstructured regular meshes the rate of convergence of approximate solutions generated by the upwind scheme towards the unique solution of the continuous model is at least one. The numerical error is estimated in terms of logarithmic Kantorovich–Rubinstein distances and provides a bound on the rate of weak convergence.
Mathematics Subject Classification: 65M08 / 65M12 / 65M15
Key words: Stability estimate / finite volume scheme / implicit upwind scheme / Kantorovich–Rubinstein distance / rate of convergence / stability / weak BV estimate
© The authors. Published by EDP Sciences, SMAI 2023
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.
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