A review of a posteriori error control and adaptivity for approximations of nonlinear conservation laws.

Ohlberger M

Abstract

In this contribution we give an overview on recent progress in obtaining a posteriori error control forfinite volume and discontinuous Galerkin approximations of non-linear hyperbolic conservation laws.The theory is based on the celebrated doubling of variables technique introduced by Kruˇzkov [35].A posteriori error control is of particular importance as it can be used for designing efficient gridadaptive schemes. The derivation of such adaptive methods is discussed and numerical experimentsare given.