Kim, Hyea Hyun; Lee, Chang-Ock; Park, Eun-Hee A FETI-DP formulation for the Stokes problem without primal pressure components. (English) Zbl 1275.76160 SIAM J. Numer. Anal. 47, No. 6, 4142-4162 (2010). Summary: A scalable FETI-DP (dual-primal finite element tearing and interconnecting) algorithm for the Stokes problem that employs a lumped preconditioner is developed and analyzed. A pair of inf-sup stable velocity and pressure finite element spaces is used to obtain a discrete problem. Differently from previous approaches, no primal pressure unknowns are selected and only velocity primal unknowns at subdomain corners are selected. This leads to a symmetric and positive definite coarse problem matrix in the FETI-DP operator, while a larger and indefinite coarse problem appears in the previous approaches. In addition, its condition number bound is proved to be the same as the FETI-DP algorithm with a lumped preconditioner for elliptic problems. Numerical results are included. Cited in 2 ReviewsCited in 17 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 76D07 Stokes and related (Oseen, etc.) flows Keywords:FETI-DP; Stokes problem; lumped preconditioner PDFBibTeX XMLCite \textit{H. H. Kim} et al., SIAM J. Numer. Anal. 47, No. 6, 4142--4162 (2010; Zbl 1275.76160) Full Text: DOI Link