The Analysis of Multigrid Algorithms for Nonconforming and Mixed Methods for Second Order Elliptic Problems

Zhangxin Chen
Department of Mathematics and
Institute for Scientific Computation
Texas A&M University
College Station, TX 77843--3404

Do Y. Kwak
Department of Mathematics
Korea Advanced Institute Science and Technology
Taejon, Korea 305--701

Abstract

In this paper we consider multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements. We prove optimal convergence properties of the W-cycle multigrid algorithm and uniform condition number estimates for the variable V-cycle preconditioner. Lower order terms are treated, so our results also apply to parabolic equations.


Contributed January 20, 1995.