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

2016/11/09 by Alexey Miroshnikov, Miroshnikov, Alexey
Computer Science · Engineering · Mathematics · #35L70 #3D Shape Modeling and Analysis #74B20 #74H15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1611.02888

openalex publication_date 2016/11/09 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28

Abstract

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

Citations

• The second law of thermodynamics and stability
• Convexity conditions and existence theorems in nonlinear elasticity

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