Skip to main content
Log in

The Solution of a Singularly Perturbed Convection–Diffusion Problem by an Iterative Domain Decomposition Method

  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

This paper deals with an iterative algorithm for domain decomposition applied to the solution of a singularly perturbed convection–diffusion problem. Convergence properties of the algorithm are established. Numerical results are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. I. Boglaev, Approximate solution of a non-linear boundary value problem with a small parameter for the highest-order derivative, Comput. Math. Math. Phys. 24 (1984) 30–35.

    Google Scholar 

  2. I. Boglaev, On a domain decomposition algorithm for a singularly perturbed reaction-diffusion problem, J. Comput. Appl. Math. 98 (1998) 213–232.

    Google Scholar 

  3. I. Boglaev and V. Sirotkin, Numerical solution of some quasi-linear singularly perturbed heat-conduction equations on nonuniform grids, Comput. Math. Math. Phys. 30 (1990) 28–40.

    Google Scholar 

  4. C. Dawson, Q. Du and T. Dupont, A finite difference domain decomposition algorithm for numerical solution of the heat equation, Math. Comp. 57 (1991) 63–71.

    Google Scholar 

  5. P. Farrell, I. Boglaev and V. Sirotkin, Parallel domain decomposition methods for semi-linear singu-larly perturbed differential equations, Comput. Fluid Dynamics J. 2 (1994) 423–433.

    Google Scholar 

  6. M. Garbey, A Schwarz alternating procedure for singular perturbation problems, SIAM J. Sci. Comput. 17 (1996) 1175–1201.

    Google Scholar 

  7. T. Mathew, Uniform convergence of the Schwarz alternating method for solving singularly perturbed advection-diffusion equations, SIAM J. Numer. Anal. 35 (1998) 1663–1683.

    Google Scholar 

  8. J. Miller, E. O'Riordan and G. Shishkin, Fitted Numerical Methods for Singular Perturbation Problems (World Scientific, Singapore, 1996).

    Google Scholar 

  9. T. Linss, H.-G. Roos and R. Vulanovic, Uniform pointwise convergent on Shishkin-type meshes for quasi-linear convection-diffusion problems, SIAM J. Numer. Anal. 38 (2000) 897–912.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boglaev, I.P. The Solution of a Singularly Perturbed Convection–Diffusion Problem by an Iterative Domain Decomposition Method. Numerical Algorithms 31, 27–46 (2002). https://doi.org/10.1023/A:1021103905345

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021103905345

Navigation