Domain Embedding Preconditioners for Mixed Systems 1

In this paper we study block diagonal preconditioners for mixed systems derived from the Dirichlet problems for second order elliptic equations. The main purpose is to discuss how an embedding of the original computational domain into a simpler extended domain can be utilized in this case. We show that a family of uniform preconditioners for the corresponding problem on the extended, or ctitious, domain leads directly to uniform preconditioners for the original problem. This is in contrast to the situation for the standard nite element method, where the domain embedding approach for the Dirichlet problem is less obvious.