Convergence of Numerical Approximations to Non-linear Continuity Equations with Rough Force Fields

F. Ben Belgacem, P. E. Jabin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 allows us to not only 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 novel commutator estimates, quantifying and extending to the non-linear case the classical commutator approach of the theory of renormalized solutions.

Original languageEnglish (US)
Pages (from-to)509-547
Number of pages39
JournalArchive for Rational Mechanics and Analysis
Volume234
Issue number2
DOIs
StatePublished - Nov 1 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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