Relative entropy based error estimates for discontinuous Galerkin schemes

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Abstract

These notes give an overview on how the relative entropy stability framework can be employed to derive a posteriori error estimates for semi-(spatially)-discrete discontinuous Galerkin schemes approximating systems of hyperbolic conservation laws endowed with one strictly convex entropy. We also show how these methods can be extended as to cover a related, higher order, model for compressible multiphase flows with non-convex energy.

Keywords

hyperbolic conservation law discontinuous Galerkin method a posteriori error analysis compressible multiphase flows relative entropy 

Mathematical subject classification

35L60 65M60 76T10 

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Copyright information

© Sociedade Brasileira de Matemática 2016

Authors and Affiliations

  1. 1.University of StuttgartStuttgartGermany

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