Implementation of Hybrid V -cycle Algebraic Multilevel Methods for Mixed Finite Element Systems with Penalty

SUMMARY The goal of this paper is the implementation of the hybrid V-cycle hierarchical algebraic multilevel methods for the indeenite discrete systems which arise when a mixed nite element approximation is used to solve elliptic boundary value problems. By introducing a penalty parameter, the perturbed indeenite system can be reduced to a symmetric positive deenite system containing the small penalty parameter for the velocity unknown alone. We stabilize the hierarchical spatial decomposition approach proposed by Cai, Goldstein and Pasciak 7] for the reduced system. We demonstrate that the relative condition number of the preconditioner is bounded uniformly with respect to the penalty parameter, the number of levels and possible jumps of the coeecients as long as they occur only across edges of coarsest elements.