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No abstract

Abstract.We first prove an abstract result for a class of nonlocal problems using fixed point method.We apply this result to equations revelant from plasma physic 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.

In this paper we study a general theory for the numerical approximation of functional nonlinear two-parameter problems in a neighbourhood of an isola center. The results are also valid for a certain class of perturbed bifurcation points. The abstract theory is applied to the Galerkin approximation of nonlinear variational posed problems. In this case, as a consequence of the error being orthogonal to the approximating space, we prove the superconvergence of the perturbation parameter, whereas for the bifurcation parameter and the solution we obtain the same order as in the linear problem. Numerical results are given for the one-dimensional Brussellator model. Subject Classification (1991): 65N30, 34A50, 65J15 Mathematics