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

Giesselmann, J. and Pryer, T. (2016) Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics. IMA Journal of Numerical Analysis, 36 (4). pp. 1685-1714. ISSN 1464-3642 doi: 10.1093/imanum/drv052

Abstract/Summary

We give an a posteriori analysis of a semidiscrete 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, SIAM J. Math. Anal., 46, 3518–3539). 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 and a set of elliptic reconstructions to apply the reduced relative entropy framework in this setting.