Factorization of the convection-diffusion operator and the Schwarz algorithm. (English) Zbl 0826.65102

Nataf, Frédéric; Rogier, François

Math. Models Methods Appl. Sci. 5, No. 1, 67-93 (1995).

A linear convection-diffusion equation of the type \({\mathcal L}u= \Delta u + v \cdot \nabla u - u = f\) is considered on a two-dimensional strip-shaped domain. The operator \(\mathcal L\) is factorized into two parabolic problems either exactly or approximately, the boundary conditions being fitted with a domain decomposition method. In the latter case, variable coefficients are admitted, too. Then the Schwarz algorithm is used as an alternative solver and the convergence rate is proved and tested on illustrative numerical examples for the domain decomposition both into strips and into rectangles.

Reviewer: T.Roubíček (Praha)

MSC:

65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N06	Finite difference methods for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
35J25	Boundary value problems for second-order elliptic equations

Keywords:

linear convection-diffusion equation; domain decomposition; Schwarz algorithm; convergence; numerical examples