Domain decomposition algorithms for mixed methods for second-order elliptic problems

Abstract

In this paper domain decomposition algorithms for mixed finite element methods for linear second-order elliptic problems in R 2 \mathbb {R}^{2} and R 3 \mathbb {R}^{3} are developed. A convergence theory for two-level and multilevel Schwarz methods applied to the algorithms under consideration is given. 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.