4.3 Article

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

Journal

BIT NUMERICAL MATHEMATICS
Volume 56, Issue 1, Pages 99-127

Publisher

SPRINGER
DOI: 10.1007/s10543-015-0560-2

Keywords

Discontinuous Galerkin finite element method; A priori error analysis; Multiphase elastodynamics; Relative entropy; Reduced relative entropy

Funding

  1. German Research Foundation (DFG) [SFB TRR 75]
  2. EPSRC [EP/H024018/1]
  3. LMS [41214]
  4. Engineering and Physical Sciences Research Council [EP/H024018/1] Funding Source: researchfish
  5. EPSRC [EP/H024018/1] Funding Source: UKRI

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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 norm for the strain and the norm for the velocity, where dG is an appropriate mesh dependent -like space.

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