Le Borne, SabineSabineLe BorneRebholz, Leo G.Leo G.Rebholz2020-02-182020-02-182015-03-01Computing and Visualization in Science 6 (16): 259-269 (2015)http://hdl.handle.net/11420/4964This paper deals with the analysis of preconditioning techniques for a recently introduced sparse grad-div stabilization of the Oseen problem. The finite element discretization error for the Oseen problem can be reduced through the addition of a grad-div stabilization term to the momentum equation of the Oseen problem. Such a stabilization has an interesting effect on the properties of the discrete linear system of equations, in particular on the convergence properties of iterative solvers. Comparing to unstabilized systems, it swaps the levels of difficulties for solving the two main subproblems, i.e., solving for the first diagonal block and solving a Schur complement problem, that occur in preconditioners based on block triangular factorizations. In this paper we are concerned with a sparse variant of grad-div stabilization which has been shown to have a stabilization effect similar to the full grad-div stabilization while leading to a sparser system matrix. Our focus lies on the subsequent iterative solution of the discrete system of equations.en1433-036920156259269Springeraugmented lagrangiangrad-div stabilizationoseen problempreconditionerschur complementsparse grad-divMathematikJournal Article10.1007/s00791-015-0236-0Other