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.
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Giesselmann, J. Relative entropy based error estimates for discontinuous Galerkin schemes. Bull Braz Math Soc, New Series 47, 359–372 (2016). https://doi.org/10.1007/s00574-016-0144-z
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DOI: https://doi.org/10.1007/s00574-016-0144-z
Keywords
- hyperbolic conservation law
- discontinuous Galerkin method
- a posteriori error analysis
- compressible multiphase flows
- relative entropy