Convergence of numerical approximations to non-linear continuity equations with rough force fields
Analysis of PDEs
2016-12-01 v1 Numerical Analysis
Abstract
We prove quantitative regularity estimates for the solutions to non-linear continuity equations and their discretized numerical approximations on Cartesian grids when advected by a rough force field. This allow us to recover the known optimal regularity for linear transport equations but also to obtain the convergence of a wide range of numerical schemes. Our proof is based on a novel commutator estimates, quantifying and extending to the non-linear case the classical commutator approach of the theory of renormalized solutions.
Cite
@article{arxiv.1611.10271,
title = {Convergence of numerical approximations to non-linear continuity equations with rough force fields},
author = {F. Ben Belgacem and P-E Jabin},
journal= {arXiv preprint arXiv:1611.10271},
year = {2016}
}