MULTILEVEL ITERATION FOR MIXED FINITE-ELEMENT SYSTEMS WITH PENALTY

In this paper, the authors consider the solution of the discrete syste ms that arises when a mixed finite element approach is used to approxi mate the solution of second-order elliptic boundary value problems. By the introduction of a penalty parameter, these equations can be appro ximated by the solution of a symmetric and positive definite penalty s ystem on the velocity subspace. Iterative procedures are developed and analyzed for this penalty system based on the hierarchical basis appr oach as well as on the standard multigrid approach. Finally, numerical experiments are presented that illustrate the convergence behavior su ggested by the theory.