Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics
arXiv:1405.4750 · doi:10.1007/s10543-015-0560-2
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.
21 pages, 2 tables