Stability of fully discrete variational schemes for elastodynamics with a polyconvex stored energy

Alexey Miroshnikov

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arXiv · 1611.02888

Stability of fully discrete variational schemes for elastodynamics with a polyconvex stored energy

Alexey Miroshnikov

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Abstract

In this article we develop a fully discrete variational scheme that approximates the equations of three dimensional elastodynamics with polyconvex stored energy. The fully discrete scheme is based on a time-discrete variational scheme developed by S.~Demoulini, D.~M.~A.~Stuart and A.~E.~Tzavaras (2001). We show that the fully discrete scheme is unconditionally stable. The proof of stability is based on a relative entropy estimation for the fully discrete approximates.

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Alexey Miroshnikov. 2016-11-09. Stability of fully discrete variational schemes for elastodynamics with a polyconvex stored energy. https://arxiv.org/abs/1611.02888

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