A conforming auxiliary space preconditioner for the mass conserving mixed stress method

Abstract

We are studying the efficient solution of the system of linear equation stemming from the mass conserving mixed stress (MCS) method discretization of the Stokes equations. To that end we perform static condensation to arrive at a system for the pressure and velocity unknowns. An auxiliary space preconditioner for the positive definite velocity block makes use of efficient and scalable solvers for conforming Finite Element spaces of low order and is analyzed with emphasis placed on the polynomial degree of the discretization. Numerical experiments demonstrate the potential of this approach and the efficiency of the implementation.