A generalized Stokes problem is addressed in the framework of a domain decomposition method, in which the physical computational domain Ω is partitioned into two subdomains Ω1 and Ω2. Three different situations are covered. In the former, the viscous terms are kept in both subdomains. Then we consider the case in which viscosity is dropped out everywhere in Ω. Finally, a hybrid situation in which viscosity is dropped out only in Ω1 is addressed. The latter is motivated by physical applications. In all cases, correct transmission conditions across the interface Γ between Ω1 and Ω2 are devised, and an iterative procedure involving the successive resolution of two subproblems is proposed. The numerical discretization is based upon appropriate finite elements, and stability and convergence analysis is carried out. We also prove that the iteration-by-subdomain algorithms which are associated with the various domain decomposition approaches converge with a rate independent of the finite element mesh size. © 1991 Springer-Verlag.
Coupling of viscous and inviscid Stokes equations via a domain decomposition method for finite elements
QUARTERONI, ALFIO MARIA;
1991-01-01
Abstract
A generalized Stokes problem is addressed in the framework of a domain decomposition method, in which the physical computational domain Ω is partitioned into two subdomains Ω1 and Ω2. Three different situations are covered. In the former, the viscous terms are kept in both subdomains. Then we consider the case in which viscosity is dropped out everywhere in Ω. Finally, a hybrid situation in which viscosity is dropped out only in Ω1 is addressed. The latter is motivated by physical applications. In all cases, correct transmission conditions across the interface Γ between Ω1 and Ω2 are devised, and an iterative procedure involving the successive resolution of two subproblems is proposed. The numerical discretization is based upon appropriate finite elements, and stability and convergence analysis is carried out. We also prove that the iteration-by-subdomain algorithms which are associated with the various domain decomposition approaches converge with a rate independent of the finite element mesh size. © 1991 Springer-Verlag.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
