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

Giesselmann, J. and Pryer, T. (2016) Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics. BIT Numerical Mathematics, 56 (1). pp. 99-127. ISSN 1572-9125

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To link to this item DOI: 10.1007/s10543-015-0560-2

Abstract/Summary

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 Giesselmann (SIAM J Math Anal 46(5):3518–3539, 2014). The estimate we derive is optimal in the L∞(0,T;dG) norm for the strain and the L2(0,T;dG) norm for the velocity, where dG is an appropriate mesh dependent H1-like space.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:47036
Uncontrolled Keywords:Discontinuous Galerkin finite element method; A priori error analysis; Multiphase elastodynamics; Relative entropy; Reduced relative entropy; 65M60; 65M12; 65M15; 74B20
Publisher:Springer

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