A discrete variational scheme for isentropic processes in polyconvex thermoelasticity
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Preprint Posting Date2019-12-12
Online Publication Date2020-06-29
Print Publication Date2020-08
Embargo End Date2021-06-29
Permanent link to this recordhttp://hdl.handle.net/10754/660719
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AbstractWe propose a variational scheme for the construction of isentropic processes of the equations of adiabatic thermoelasticity with polyconvex internal energy. The scheme hinges on the embedding of the equations of adiabatic polyconvex thermoelasticity into a symmetrizable hyperbolic system. We establish existence of minimizers for an associated minimization theorem and construct measure-valued solutions that dissipate the total energy. We prove that the scheme converges when the limiting solution is smooth.
CitationChristoforou, C., Galanopoulou, M., & Tzavaras, A. E. (2020). A discrete variational scheme for isentropic processes in polyconvex thermoelasticity. Calculus of Variations and Partial Differential Equations, 59(4). doi:10.1007/s00526-020-01766-w
SponsorsThe authors thank the anonymous referee for very helpful comments that helped considerably in improving this work.