Error estimates for a finite volume scheme for advectiondiffusion equations with rough coefficients
Abstract
We study the implicit upwind finite volume scheme for numerically approximating the advectiondiffusion equation with a vector field in the low regularity DiPernaLions 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 advectiondiffusion equation with a vector field in the low regularity DiPernaLions 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 KantorovichRubinstein distances and provides thus a bound on the rate of weak convergence.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 arXiv:
 arXiv:2201.10411
 Bibcode:
 2022arXiv220110411N
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Numerical Analysis
 EPrint:
 27 pages