Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamicsGiesselmann, 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 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1093/imanum/drv052 Abstract/SummaryWe 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.
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