A Multigrid Algorithm for Hybridized Finite Element Methods

PDE (partial differential equation) arises in various areas modeling physical, biological, and engineering applications. Hence it is not surprising that solution techniques for PDEs form one of the most important research fields in mathematics. FEM (finite element method) is a very important numerical method to solve PDE. Hybridized FEM provides a lot more advantages compared to tradition FEM, but it still generates a matrix system whose condition number depends on mesh size, which deteriorates the performance of classical iterative algorithms, such as conjugate gradient method. In this case, multigrid method comes as rescue, since it provide a convergence process independent of mesh size, but there are some new challenges to face when adapting it to the hybridized FEM. In this talk, a newly developed successful multigrid V-cycle algorithm for hybridized FEM will be introduced, and some numerical experiment results will be presented.