A FETI-DP FORMULATION FOR THE STOKES PROBLEM WITHOUT PRIMAL PRESSURE COMPONENTS

Abstract

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.