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We first prove an abstract result for a class of nonlocalproblems using fixed point method. We apply this result toequations revelant from plasma physic problems. These equationscontain terms like monotone or relative rearrangement of functions.So, we start the approximation study by using finite element todiscretize this nonstandard quantities. We end the paper by giving a numerical resolution of a model containing those terms.

We illustrate how some interesting new variational principles can beused for the numerical approximation of solutions to certain (possiblydegenerate) parabolic partial differential equations. One remarkablefeature of the algorithms presented here is that derivatives do notenter into the variational principles, so, for example, discontinuousapproximations may be used for approximating the heat equation. Wepresent formulae for computing a Wasserstein metric which entersinto the variational formulations.

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Numerical Approximations of the Relative Rearrangement:The piecewise linear case.Application to some Nonlocal Problems

Approximation of Parabolic EquationsUsing the Wasserstein Metric

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2 results

Numerical Approximations of the Relative Rearrangement:The piecewise linear case.Application to some Nonlocal Problems

Approximation of Parabolic EquationsUsing the Wasserstein Metric