Continuous preconditioners for the mixed Poisson problem (Q766221)

The author shows that preconditioners designed for piecewise linear finite element discretizations of the Poisson problem can be used as preconditioners for the mixed problem. The proposed preconditioner can be applied both to the original and to the reduced Schur complement problem. The author proves that iterations required to solve the preconditioned system will have the same dependency on the mesh size as for the preconditioner applied to the Poisson problem with a suitable iterative method (e.g., the conjugate-gradient (method). The author also gives numerical examples, which demonstrate the effectiveness of the proposed preconditioner.