Numerical methods for singularly perturbed elliptic problems containing two perturbation parameters¹

This research was supported in part by the National Center for Plasma Science and Technology Ireland and by the Russian Foundation for Basic Research grant No. 04–01–00578.

Abstract

A priori parameter explicit bounds on the derivatives of the solution of a two parameter singularly perturbed elliptic problem in two space dimensions are presented. These bounds are used to establish parameter uniform error bounds for a numerical method consisting of upwinding on a tensor product of two piecewise uniform meshes.

Key words:

• Elliptic
• two parameters
• a priori bounds

Notes

This research was supported in part by the National Center for Plasma Science and Technology Ireland and by the Russian Foundation for Basic Research grant No. 04–01–00578.