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

Jan Giesselmann, Tristan Pryer

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Abstract

We give an a priori 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 [Gie14]. We prove optimal bounds for the strain in an appropriate norm and suboptimal bounds for the velocity.
Original languageEnglish
Pages (from-to)99-127
Number of pages30
JournalBIT Numerical Mathematics
Volume56
Issue number1
Early online date15 Jul 2015
DOIs
Publication statusPublished - 31 Mar 2016

Keywords

  • math.NA

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