Domain Decomposition Algorithms for Mixed
Methods for Second Order Elliptic Problems

Zhangxin Chen, Richard E. Ewing, and Raytcho Lazarov
Department of Mathematics and
Institute for Scientific Computation
Texas A&M University
College Station, TX 77843

Abstract

In this paper domain decomposition algorithms for mixed finite element methods for linear and quasilinear second order elliptic problems are developed. A convergence theory for two-level and multilevel Schwarz methods applied to the algorithms under consideration is given, and its extension to other substructuring methods such as vertex space and balancing domain decomposition methods is considered. It is shown that the condition number of these iterative methods is bounded uniformly from above in the same manner as in the theory of domain decomposition methods for conforming and nonconforming finite element methods for the same differential problems. Numerical experiments are presented to illustrate the present techniques.


Contributed December 22, 1994.