Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics

Jan Giesselmann, Tristan Pryer

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Abstract

We give an a posteriori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in [Giesselmann 2014]. This framework allows energy type arguments to be applied to continuous functions. Since we advocate the use of discontinuous Galerkin methods we make use of two families of reconstructions, one set of discrete reconstructions [Makridakis and Nochetto 2006] and a set of elliptic reconstructions [Makridakis and Nochetto 2003] to apply the reduced relative entropy framework in this setting.
Original languageEnglish
Pages (from-to)1685-1714
Number of pages30
JournalIMA Journal of Numerical Analysis
Volume36
Issue number4
Early online date21 Oct 2015
DOIs
Publication statusPublished - 31 Oct 2016

Keywords

  • math.NA

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