$\mathcal{K}-$convergence as a new tool in numerical analysis
Numerical Analysis
2019-04-02 v1
Abstract
We adapt the concept of convergence of Young measures to the sequences of approximate solutions resulting from numerical schemes. We obtain new results on pointwise convergence of numerical solutions in the case when solutions of the limit continuous problem possess minimal regularity. We apply the abstract theory to a finite volume method for the isentropic Euler system describing the motion of a compressible inviscid fluid. The result can be seen as a nonlinear version of the fundamental Lax equivalence theorem.
Keywords
Cite
@article{arxiv.1904.00297,
title = {$\mathcal{K}-$convergence as a new tool in numerical analysis},
author = {Eduard Feireisl and Maria Lukacova-Medvidova and Hana Mizerova},
journal= {arXiv preprint arXiv:1904.00297},
year = {2019}
}