Domain decomposition methods for systems of conservation laws: Spectral collocation approximations. (English) Zbl 0711.65082

Quarteroni, Alfio

SIAM J. Sci. Stat. Comput. 11, No. 6, 1029-1052 (1990).

The author proposes an effective domain decomposition method for the numerical solution of quasi-linear hyperbolic systems of conservation laws. The method is designed for a general nonlinear problem in several space variables. Convergence analysis is carried out and the precise form of the error-reduction factor is derived. An application of the proposed method is indicated.

Reviewer: P.K.Mahanti

MSC:

65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L65	Hyperbolic conservation laws

Keywords:

spectral collocation; domain decomposition method; quasi-linear hyperbolic systems of conservation laws; Convergence; error-reduction factor