A domain decomposition method derived from the Primal Hybrid Formulations for 2nd order elliptic problems

Abstract

We consider the primal hybrid formulation for second order elliptic problems introduced by Raviart-Thomas and apply the classical iterative method of Uzawa to obtain a non overlapping domain decomposition method that converges geometrically with a mesh independent ratio. The proposed method connects with the Finite Element Tearing and Interconnecting (FETI) method proposed by Farhat-Roux and collaborators. In this research work we use the detailed work on domains with corners developed by Grisvard [6], which clarifies the situation of cross-points, and the direct computation of the duality H−1/2 − H1/2 using the H1/2 scalar product; therefore no consistency error appears.