Department of Mathematics, University of Delaware
szhang@math.udel.eduThe multigrid method is an effective iterative algorithm for solving linear systems of equations arising from boundary value problems. The multigrid method has been recently applied extensively and studied intensively due to its optimal-order computational complexity, i.e. the number of operations is proportional to the number of unknowns in the linear system. In this talk, we will discuss some unusual features of the multigrid method when applied to the stationary Stokes equation, where the multilevel finite (mixed) element spaces may not be nested due to special structures of the elements or the underlying grids. We will show also the effectiveness of a multigrid version of a iterated penalty method (a Uzawa's algorithm) when applied to the mixed-element Stokes equation if the discrete spaces for the pressure are precisely the divergence of the finite element spaces for the velocity.