Abstract: Combined hybrid finite elements method, applied to linear elasticity problem, is a stabilized finite element method. It is a large sparse symmetric positive definite system arising from combined hybrid quadrilateral element discretization. In order to solve the system quickly, the multigrid preconditioned conjugate gradient method (MGCGM) is introduced in this paper. Firstly, by choosing the appropriate intergrid transfer operators and smoothing strategy, an effective multigrid preconditioner is obtained. Then, numerical results show that MGCGM proposed is efficient, that is the condition number of the stiffness matrix is greatly decreased by the multigrid preconditioner. Moreover, the method still has a good convergence for the combined hybrid element with high performance in the case of the mesh distortion.

Key words: combined hybrid element, Wilson interpolation, intergrid transfer operator, multigrid method, preconditioned conjugate gradient method