Block triangular preconditioners for stabilized saddle point problems with nonsymmetric (1,1)-block

We study the performance of a class of block triangular preconditioners for saddle point systems with nonsymmetric positive definite (1,1)-block. The presented results incorporate the established results in Zhang and Zhao (2018) where a (parameter-dependent) preconditioner was suggested to solve the mentioned saddle point systems. The performance of the preconditioner in conjunction with Krylov subspace methods is examined for solving a test problem arising from stabilized finite element discretizations of the Oseen problem. The reported numerical experiments show that there exist parameter free preconditioners which outperform the preconditioner proposed in the earlier referred work.