Numerical approximations of the relative rearrangement: the piecewise linear case. Application to some nonlocal problems

We first prove an abstract result for a class of nonlocal problems using fixed point method. We apply this result to equations relevant from plasma physics problems. These equations contain terms like monotone or relative rearrangement of functions. So, we start the approximation study by using finite element to discretize this nonstandard quantities. We end the paper by giving a numerical resolution of a model containing those terms. (author)