A Multigrid Algorithm Of Immersed Interface Finite Element Methods For The Second-order Elliptic Interface Problem

In this dissertation, we propose a multigrid algorithm of the immersed interface finite element method for the second-order elliptic interface problem.First of all, we briefly introduce the immersed interface finite element method for the second-order elliptic interface problem. Nex-t, we give the intergrid transfer operator between a coarse grid space and a fine grid space, and prove the stability and the approxima-tive property of the intergrid transfer operator. Then, we propose a W-cycle multigrid algorithm, and prove the smoothness and the ap-proximative property, and show the optimal convergence of W-cycle multigrid algorithm. Finally, numerical experiments are presented to confirm our theoretical results.