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On the convergence of basic iterative methods for convection–diffusion equations

✍ Scribed by Jürgen Bey; Arnold Reusken

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
144 KB
Volume
6
Category
Article
ISSN
1070-5325

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✦ Synopsis

In this paper we analyze convergence of basic iterative Jacobi and Gauss-Seidel type methods for solving linear systems which result from finite element or finite volume discretization of convection-diffusion equations on unstructured meshes. In general the resulting stiffness matrices are neither M-matrices nor satisfy a diagonal dominance criterion. We introduce two new matrix classes and analyse the convergence of the Jacobi and Gauss-Seidel methods for matrices from these classes. A new convergence result for the Jacobi method is proved and negative results for the Gauss-Seidel method are obtained. For a few well-known discretization methods it is shown that the resulting stiffness matrices fall into the new matrix classes.

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