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We give an a posteriori analysis of a semi-discrete discontinuous Galerkinscheme approximating solutions to a model of multiphase elastodynamics, whichinvolves an energy density depending not only on the strain but also the straingradient. A key component in the analysis is the reduced relative entropystability framework developed in [Giesselmann 2014]. This framework allowsenergy type arguments to be applied to continuous functions. Since we advocatethe use of discontinuous Galerkin methods we make use of two families ofreconstructions, one set of discrete reconstructions [Makridakis and Nochetto2006] and a set of elliptic reconstructions [Makridakis and Nochetto 2003] toapply the reduced relative entropy framework in this setting.

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