Showing a limited preview of this publication:
The standard conforming finite element methods on one type of highly nonuniform rectangular meshes are considered for solving the quasilinear singular perturbation problem -ε2(uxx + uyy ) + ƒ(x,y;u) = 0. By using a special interpolation operator and the integral identity technique, optimal uniform convergence rates of O(N–(k+1)) in the L2-norm are obtained for all k-th (k ≥ 1) order conforming tensor-product finite elements, where N is the number of intervals in both x- and y-directions. Hence Apel and Lube's suboptimal results are improved to optimal order and generalized to the quasilinear case.
Published Online: 2004-04-01
Published in Print: 2004-04-01
Copyright 2004, Walter de Gruyter
