Goal-oriented error analysis of a DG scheme for a second gradient elastodynamics model

Giesselmann, J. and Pryer, T. (2017) Goal-oriented error analysis of a DG scheme for a second gradient elastodynamics model. In: Cancès, C. and Omnes, P. (eds.) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects: FVCA 8, Lille June 2017: conference proceedings. Springer Proceedings in Mathematics & Statistics (199). Springer, pp. 457-466. doi: 10.1007/978-3-319-57397-7_39

Abstract/Summary

In this note we propose a discontinuous Galerkin in space, continuous Galerkin in time method for a problem arising in elastodynamics with phase transition. We make use of a dispersion operator from [BCKX11] allowing us to construct a consistent scheme. We derive goal-oriented a posteriori error estimators for this scheme based on dual weighted residuals. We conclude by summarising extensive numerical experiments.