A Global Uniformly Convergent Finite Element Method for a Quasilinear Singularly Perturbed Elliptic Problem

Jichun Li, I. M. Navon

In this paper, we construct a bilinear finite element method based on a special piecewise uniform mesh for solving a quasilinear singularly perturbed elliptic problem in two space dimensions. A quasi-optimal global uniform convergence rate $O(N_x^{-2}\ln ^2 N_x+N_y^{-2}\ln ^2 N_y)$ 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.