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

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−2x ln2 Nx + N−2y ln2 Ny) was obtained, which is independent of the perturbation parameter. Here Nx and Ny are the number of elements in the x-and y-directions, respectively.