Abstract
In this paper, a class of singularly perturbed elliptic partial differential equations posed on a rectangular domain is studied. The differential equation contains two singular perturbation parameters. The solutions of these singularly perturbed problems are decomposed into a sum of regular, boundary layer and corner layer components. Parameter-explicit bounds on the derivatives of each of these components are derived. A numerical algorithm based on an upwind finite difference operator and a tensor product of piecewise-uniform Shishkin meshes is analysed. Parameter-uniform asymptotic error bounds for the numerical approximations are established.
Original language | English |
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Pages (from-to) | 57-82 |
Number of pages | 26 |
Journal | Advances in Computational Mathematics |
Volume | 35 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jul 2011 |