VARIATIONAL PARTICLE SCHEMES FOR THE POROUS MEDIUM EQUATION AND FOR THE SYSTEM OF ISENTROPIC EULER EQUATIONS

We introduce variational particle schemes for the porous medium equation and the system of isentropic Euler equations in one space dimension. The methods are motivated by the interpretation of each of these partial differential equations as a 'steepest descent' on a suitable abstract manifold. We show that our methods capture very well the nonlinear features of the flows.

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