Dual-Variable Schwarz Methods for Mixed Finite Elements

Abstract

Schwarz methods for the mixed finite element discretization of second order elliptic problems are considered. By using an equivalence between mixed methods and conforming spaces first introduced in [13], it is shown that the condition number of the standard additive Schwarz method applied to the dual-variable system grows at worst like O(1+H/delta) in both two and three dimensions and for elements of any order. Here, H is the size of the subdomains, and delta is a measure of the overlap. Numerical results are presented that verify the bound