A global uniformly convergent finite element method for a quasi-linear singularly perturbed elliptic problem

Abstract

In this paper, we construct a bilinear finite element method based on a special piecewise uniform mesh for solving a quasi-linear singularly perturbed elliptic problem in two space dimensions. A quasi-optimal global uniform convergence rate O( N −2 x ln 2 N x + N −2 y ln 2 N y ) was obtained, which is independent of the perturbation parameter. Here N x and N y are the number of elements in the x-and y-directions, respectively.