Petrov-Galerkin Method with Local Green's Functions in Singularly Perturbed Convection-Diffusion Problems

Petrov-Galerkin Method with Local Green's Functions in Singularly Perturbed Convection-Diffusion Problems

Year:    2005

International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 2 : pp. 127–146

Abstract

Previous theoretical and computational investigations have shown high efficiency of the local Green's function method for the numerical solution of singularly perturbed problems with sharp boundary layers. However, in several space variables those functions, used as projectors in the Petrov-Galerkin scheme, cannot be derived in a closed analytical form. This is an obstacle for the application of the method when applied to multi-dimensional problems. The present work proposes a semi-analytical approach to calculate the local Green's function, which opens a way to effective practical application of the method. Besides very accurate approximation, the matrix stencils obtained with these functions allow the use of fast and stable iterative solution of the large sparse algebraic systems that arise from the grid-discretization. The advantages of the method are illustrated by numerical examples.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2005-IJNAM-925

International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 2 : pp. 127–146

Published online:    2005-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    convection-diffusion equation Petrov-Galerkin discretization Fourier transform integral equations iterative solution.