论文信息 - A Uniformly Convergent Galerkin Method on a Shishkin Mesh for a Convection-Diffusion Problem

A Uniformly Convergent Galerkin Method on a Shishkin Mesh for a Convection-Diffusion Problem

Received September 16, 1996A Galerkin finite element method that uses piecewise bilinears on a simplepiecewise equidistant mesh is applied to a linear convection-dominatedconvection-diffusion problem in two dimensions. The method is shown to beconvergent, uniformly in the perturbation parameter, of order

U MartinStynes

[1] R. B. Kellogg,et al. Differentiability properties of solutions of the equation -ε 2 δ u + ru = f ( x,y ) in a square , 1990 .

[2] John J. H. Miller. Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions , 1996 .

[3] Andrew R. Mitchell,et al. Finite Element Analysis and Applications , 1985 .

[4] M. Stynes,et al. A globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions , 1991 .

[5] M. Stynes,et al. Numerical methods for singularly perturbed differential equations : convection-diffusion and flow problems , 1996 .