Volume 2, Issue 2
Petrov-Galerkin Method with Local Green's Functions in Singularly Perturbed Convection-diffusion Problems

O. Axelsson, E. Glushkov & N. Glushkova


Int. J. Numer. Anal. Mod., 2 (2005), pp. 127-146

Published online: 1970-01

Preview Full PDF 0 765
Export citation
  • 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.

  • Keywords

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

  • AMS Subject Headings

65F10 65N22 65R10 65R20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
Copy to clipboard
The citation has been copied to your clipboard