FETI-DP preconditioners for a staggered discontinuous Galerkin formulation of the two-dimensional Stokes problem

In this paper, a class of FETI-DP preconditioners is developed for a fast solution of the linear system arising from staggered discontinuous Galerkin discretization of the two-dimensional Stokes equations. The discretization has been recently developed and has the distinctive advantages that it is optimally convergent and has a good local conservation property. In order to efficiently solve the linear system, two kinds of FETI-DP preconditioners, namely, lumped and Dirichlet preconditioners, are considered and analyzed. Scalable bounds C(H/h)C(H/h) and C(1+log(H/h))2C(1+log(H/h))2 are proved for the lumped and Dirichlet preconditioners, respectively, with the constant CC depending on the inf–sup constant of the discrete spaces but independent of any mesh parameters. Here H/hH/h stands for the number of elements across each subdomain. Numerical results are presented to confirm the theoretical estimates.