Fast multilevel solvers for a class of discrete fourth order parabolic problems (Q334328)

The paper studies fast iterative solvers for a class of two-by-two block linear systems which correspond to some discrete fourth-order parabolic equations by using mixed finite element methods. A consistent mass matrix is used in the discretization and a lumped mass matrix is used to construct efficient preconditioners. The spectrum bound of the preconditioned system and the convergence rate of the preconditioned GMRES method are established. Numerical experiments indicate that preconditioned GMRES method converges uniformly with respect to the mesh size and diffusion coefficients.