  In this paper, we study fast iterative solvers for the solution of fourth
order parabolic equations discretized by mixed finite element methods. We
propose to use consistent mass matrix in the discretization and use lumped mass
matrix to construct efficient preconditioners. We provide eigenvalue analysis
for the preconditioned system and estimate the convergence rate of the
preconditioned GMRes method. Furthermore, we show that these preconditioners
only need to be solved inexactly by optimal multigrid algorithms. Our numerical
examples indicate that the proposed preconditioners are very efficient and
robust with respect to both discretization parameters and diffusion
coefficients. We also investigate the performance of multigrid algorithms with
either collective smoothers or distributive smoothers when solving the
preconditioner systems.

Numerical Analysis