A review of a posteriori error control and adaptivity for approximations of non-linear conservation laws. (English) Zbl 1185.65163
Summary: We give an overview on recent progress in obtaining a posteriori error control for finite volume and discontinuous Galerkin approximations of non-linear hyperbolic conservation laws. The theory is based on the celebrated doubling of variables technique introduced by S. N. Kruzhkov [Math. USSR, Sb. 10, 217–243 (1970; Zbl 0215.16203)]. A posteriori error control is of particular importance as it can be used for designing efficient grid adaptive schemes. The derivation of such adaptive methods is discussed and numerical experiments are given.
MSC:
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
Keywords:
a posteriori error estimates; finite volume method; discontinuous Galerkin; hyperbolic conservation laws; adaptive schemesCitations:
Zbl 0215.16203Software:
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