A discrete variational scheme for isentropic processes in polyconvex thermoelasticity
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ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2020-06-29Preprint Posting Date
2019-12-12Online Publication Date
2020-06-29Print Publication Date
2020-08Embargo End Date
2021-06-29Submitted Date
2019-12-12Permanent link to this record
http://hdl.handle.net/10754/660719
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We 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.Citation
Christoforou, 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-wSponsors
The authors thank the anonymous referee for very helpful comments that helped considerably in improving this work.Publisher
Springer Science and Business Media LLCarXiv
1912.05835Additional Links
http://link.springer.com/10.1007/s00526-020-01766-wae974a485f413a2113503eed53cd6c53
10.1007/s00526-020-01766-w