Constraint Preconditioning for the Coupled Stokes--Darcy System

Abstract

The use of a constraint (indefinite) preconditioner for the iterative solution of the linear system arising from the finite element discretization of coupled Stokes--Darcy flow is studied. Spectral and field-of-values bounds for the preconditioned system which are independent of the underlying mesh size are presented. Numerical experiments on several two- and three-dimensional problems illustrate the effectiveness of our approach.