Calculus of Variations and Geometric Measure Theory
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F. Cavalletti - M. Sedjro - M. Westdickenberg

A Variational Time Discretization for Compressible Euler Equations

created by cavallett on 22 Oct 2014
modified on 29 Jan 2015



Inserted: 22 oct 2014
Last Updated: 29 jan 2015

Year: 2014


We introduce a variational time discretization for the multi-dimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each timestep requires the minimization of a functional measuring the acceleration of fluid elements, over the cone of monotone transport maps. We prove convergence to measure-valued solutions for the pressureless gas dynamics and the compressible Euler equations. For one space dimension, we obtain sticky particle solutions for the pressureless case.


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