Convergence of approximate solutions of conservation laws
This is a review and incremental contribution for researchers in numerical analysis and PDEs, providing a survey and some new results on convergence of numerical methods for conservation laws.
The paper reviews historical developments in convergence of approximate solutions to conservation laws since the 1950s, presents the authors' own results on numerical approximation convergence, and discusses recent work and open problems.
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.