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 fi xed point method. We apply this result to equations revelant from plasma ph ysic problems. These equations contain terms like monotone or relative rear rangement of functions. So, we start the approximation study by using finit e element to discretize this nonstandard quantities. We end the paper by gi ving a numerical resolution of a model containing those terms.