7 citations · 25 across the 10 of their papers we have counts for
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Stability of fully discrete variational schemes for elastodynamics with a polyconvex stored energy
Alexey Miroshnikov
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…
Weak* Solutions II: The Vacuum in Lagrangian Gas Dynamics
Alexey Miroshnikov, Robin Young
We develop a framework in which to make sense of solutions containing the vacuum in Lagrangian gas dynamics. At and near vacuum, the specific volume becomes infinite and enclosed v…
Weak* solutions I: A new perspective on solutions to systems of conservation laws
Alexey Miroshnikov, Robin Young
We introduce a new notion of solution, which we call weak* solutions, for systems of conservation laws. These solutions can be used to handle singular situations that standard weak…
Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy
Alexey Miroshnikov, Athanasios E. Tzavaras
We consider a variational scheme developed by S. Demoulini, D. M. A. Stuart and A. E. Tzavaras [Arch. Ration. Mech. Anal. 157 (2001)] that approximates the equations of three dimen…
Relative entropy in hyperbolic relaxation for balance laws
Alexey Miroshnikov, Konstantina Trivisa
We present a general framework for the approximation of systems of hyperbolic balance laws. The novelty of the analysis lies in the construction of suitable relaxation systems and…
A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of Jacobians
Alexey Miroshnikov, Athanasios E. Tzavaras
We consider the equations describing the dynamics of radial motions for isotropic elastic materials; these form a system of non-homogeneous conservation laws. We construct a variat…