Convergence of approximate solutions of conservation laws
Sebastian Noelle, Michael Westdickenberg
TL;DR
This paper reviews the historical development and analytical tools for convergence of approximate solutions to conservation laws, presents new results on numerical approximation convergence, and discusses recent work and open problems.
Contribution
It introduces new results on the convergence of numerical approximations for conservation laws and discusses recent developments and open questions in the field.
Findings
New convergence results for numerical schemes
Historical overview of conservation law approximations
Discussion of open problems in the field
Abstract
In this paper we consider convergence of approximate solutions of conservation laws. We start with an overview over the historical developments since the 1950s, and the analytical tools used in this context. Then we present some of our own results on the convergence of numerical approximations, discuss recent related work and open problems.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Advanced Numerical Methods in Computational Mathematics