Macro Hybrid Elements and Domain Decomposition Methods

摘要

The aim of this paper is to present a three-field formulation for linear ellipticproblems which is particularly well suited for domain decomposition methods. The formulation is inspired by the hybrid formulation of Tong for elasticity problems, the main difference being that we work here at the macro-element (subdomain) level instead of working at the element level. The effect of this is that we obtain a new formulation of the continuous problem which can then be discretized in many different ways, including the possibility of using different methods (or the same method with different meshes) from one subdomain to another. Hence, we get a fairly general framework in which most of the domain decomposition methods using non overlapping subdomains can be reinterpreted. At the end of the paper we also propose a continuous preconditioner that seems particularly appealing for dealing with nonsymmetric problems and unstructured decompositions.