An optimal Robin-Robin domain decomposition method for Stokes equations

In this paper, we develop a nonoverlapping domain decomposition method for Stokes equations by mixed finite elements with discontinuous pressures. Both conforming and nonconforming finite element spaces are considered for velocities. With Robin boundary condition set on the interface, the indefinite Stokes problem is reduced to a positive definite problem for the interface Robin transmission data by a Schur complement procedure. Choosing an appropriate relaxation parameter and two parameters in the Robin boundary conditions, the algorithm may be proved optimal. Based on the Robin-type domain decomposition method, a new preconditioner for the Stokes problem is proposed. Numerical results are given to support our theoretical findings. (C) 2021 Published by Elsevier B.V. on behalf of IMACS.

Automated summary

This paper presents a nonoverlapping domain decomposition method for Stokes equations using mixed finite elements with discontinuous pressures. Both conforming and nonconforming finite element spaces are considered for velocities. By employing Robin boundary conditions, the indefinite Stokes problem is reduced to a positive definite problem for the interface Robin transmission data. A new preconditioner for the Stokes problem is proposed based on the Robin-type domain decomposition method, with numerical results provided to support the theoretical findings.