Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients
Abstract
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 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. 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 thus a bound on the rate of weak convergence.
Keywords
Cite
@article{arxiv.2201.10411,
title = {Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients},
author = {Víctor Navarro-Fernández and André Schlichting},
journal= {arXiv preprint arXiv:2201.10411},
year = {2023}
}
Comments
27 pages. Revised version with improved main result uniform in the diffusion constant