Domain Embedding And The Dirichlet Problem

In this paper we study domain embedding preconditioners for discrete linear systems approximating the Dirichlet problem associated a second order elliptic equation. We observe that if a mixed finite element discretization is used, then such a preconditioner can be constructed in a straightforward manner from the H(div)-inner product. We also use the H(div)-inner product to construct a new preconditioner for the Lagrange multiplier system