213 IGPM213.pdf        May 2002
TITLE Convergence Analysis of the Gauss-Seidel Method for Discretized One Dimensional Euler Equations
AUTHORS Arnold Reusken
ABSTRACT We consider the nonlinear system of equations that results from the Van-Leer vector splitting discretization of the one dimensional Euler equations. This nonlinear system is linearized at the discrete solution. The main topic of this paper is a convergence analysis of block- Gauss-Seidel methods applied to this linear system of equations. Both the lexicographic and the symmetric block-Gauss-Seidel method are considered. We derive results which quantify the quality of these methods as preconditioners. These results show, for example, that for the subsonic case the symmetric Gauss-Seidel method can be expected to be a much better preconditioner than the lexicographic variant. Sharp bounds for the condition number of the preconditioned matrix are derived.
KEYWORDS Gauss-Seidel method, Euler equations, convergence analysis
DOI 10.1137/S0036142902407393
PUBLICATION SIAM journal on numerical analysis
41, 1388-1405 (2003)