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

Jan Giesselmann; Tristan Pryer

doi:10.1007/s10543-015-0560-2

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

Jan Giesselmann, Tristan Pryer

Department of Mathematical Sciences

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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 language	English
Pages (from-to)	99-127
Number of pages	30
Journal	BIT Numerical Mathematics
Volume	56
Issue number	1
Early online date	15 Jul 2015
DOIs	https://doi.org/10.1007/s10543-015-0560-2
Publication status	Published - 31 Mar 2016

Bibliographical note

21 pages, 2 tables

Keywords

math.NA

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10.1007/s10543-015-0560-2

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This is a post-peer-review, pre-copyedit version of an article published in BIT Numer Math. The final authenticated version is available online at: https://doi.org/10.1007/s10543-015-0560-2
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Cite this

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

Abstract

Bibliographical note

Keywords

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