A parameter-uniform numerical method for a singularly perturbed two parameter elliptic problem

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, boundar...

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Bibliographic Details
Published in:Advances in computational mathematics 2011-07, Vol.35 (1), p.57-82
Main Authors: O’Riordan, E., Pickett, M. L.
Format: Article
Language:English
Subjects:
Approximation
Asymptotic properties
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Corners
Derivatives
Differential equations
Mathematical analysis
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Numerical analysis
Visualization
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Summary: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.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-010-9164-1