Iterative solvers for hybridized finite element methods.

摘要

We consider the application of a variable V-cycle multigrid algorithm for the hybridized mixed method for second order elliptic boundary value problems. Our algorithm differs from previous works on multigrid for the mixed method in that it is targeted at efficiently solving the matrix system for the Lagrange multiplier of the method. Since the mixed method is best implemented by first solving for the Lagrange multiplier and recovering the remaining unknowns locally, our algorithm is more useful in practice. The critical ingredient in the algorithm is a suitable intergrid transfer operator. We design such an operator and prove mesh independent convergence of the variable V-cycle algorithm. We then extend this multigrid framework to the hybridized local discontinuous Galerkin method, and yield similar mesh independent convergence results. Numerical experiments are presented to indicate the asymptotically optimal performance of our algorithm, as well as the performance comparison among different hybridized finite element methods for targeted problems. (Full text of this dissertation may be available via the University of Florida Libraries web site. Please check http://www.uflib.ufl.edu/etd.html)