Cascadic Multigrid Method For Mortar Finite Element Approximation For Parabolic Problem

The mortar finite element is a new type of domain decomposition method, in which the subdomain meshes may be separately constructed and nonmatching along the interface. Hence it is an effective method for the problems which are singular or whose coefficients vary rapidly. Multigrid method is a nested iteration, wherein the computed solution on the previous level serves as starting point for the iteration on the new level. A typical distinction of different types of multigrid method is made by the number of correction cycles on each level: W- cycles when the number is two, V-cycles when the number is one. Cascadic multigrid is a new type of multigrid method, which requires no coarse grid corrections at all that is the number of correction cycles is zero and may be viewed as an"one way"multigird. Recently, Xu Xuejun and Chen Jinru have proposed a multigrid for the mortar element method for parabolic problems. That is, the mortar finite element method for parabolic is presented and multigrid method is used for solving the resulting discrete system.In this paper, the result for the classical multigrid method proposed by Xu Xuejun and Chen Jinru has been extended to the case of cascadic multigrid method. We consider the parabolic problems also. The mortar element method for P₁ conforming element and P₁ nonconforming element for parabolic problem is presented. A cascadic multigrid method is proposed for solving the resulting discrete system. The optimal convergence accuracy and computation complexity are established. Finally, we carry out the numerical experiments for the case of P₁ conforming element by using Richardson iteration as a smoother. Numerical experiments show that the method is effective.