Loading...
A Nonoverlapping Domain Decomposition Method for Incompressible Stokes Equations with Continuous Pressures
Li, Jing Tu, Xuemin
Li, Jing
Tu, Xuemin
Citations
Altmetric:
Abstract
A nonoverlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the proposed algorithm, Lagrange multipliers are used to enforce continuity of the velocity component across the subdomain boundary. The continuity of the pressure component is enforced in the primal form, i.e., neighboring subdomains share the same pressure degrees of freedom on the subdomain interface and no Lagrange multipliers are needed. After eliminating all velocity variables and the independent subdomain interior parts of the pressures, a symmetric positive semidefinite linear system for the subdomain boundary pressures and the Lagrange multipliers is formed and solved by a preconditioned conjugate gradient method. A lumped preconditioner is studied and the condition number bound of the preconditioned operator is proved to be independent of the number of subdomains for fixed subdomain problem size. Numerical experiments demonstrate the convergence rate of the proposed algorithm.
Description
This is the publisher's version, also available electronically from http://epubs.siam.org/doi/abs/10.1137/120861503
Date
2013
Journal Title
Journal ISSN
Volume Title
Publisher
Society for Industrial and Applied Mathematics
Collections
Research Projects
Organizational Units
Journal Issue
Keywords
Domain decomposition, Incompressible stokes, Feti-dp, Bddc
Citation
Jing Li, Xuemin Tu. (2013). A non-overlapping domain decomposition method for incompressible Stokes equations with continuous pressures. SIAM Journal on Numerical Analysis 51:1235-1253. http://www.dx.doi.org/10.1137/120861503