Solution of Nonlinear Random Partial Differential Equations by Using Finite Element Method

Abstract

In this paper, a new technique is proposed to solve some classes of nonlinear random partial differential equations using finite element method. Through this technique we were able to deal with the random variable in the presence of a nonlinear function. The idea of this technique is based on assuming that the nodal coefficients are functions of the random variable. Then by discretization of the random variable and using fitting over the discretized values of the random variable, and utilizing the shape functions of the finite element method, we get the approximate solution as a function in both space and random variable. Some numerical examples, in different domains, are presented to show the effectiveness of this technique.