A unified FETI-DP approach for incompressible Stokes equations

TL;DR

This paper introduces a unified FETI-DP framework for incompressible Stokes equations that accommodates both continuous and discontinuous pressures, simplifying analysis and demonstrating scalable convergence through numerical experiments.

Contribution

It presents a novel unified FETI-DP framework that handles both pressure types and simplifies the analysis of existing algorithms for incompressible Stokes equations.

Findings

Scalable convergence rates proved for the algorithms.

Numerical experiments confirm the effectiveness of the unified framework.

The framework simplifies the analysis of multiple FETI-DP algorithms.

Abstract

A unified framework of FETI-DP algorithms is proposed for solving the system of linear equations arising from the mixed finite element approximation of incompressible Stokes equations. A distinctive feature of this framework is that it allows using both continuous and discontinuous pressures in the algorithm, while previous FETI-DP methods only apply to discontinuous pressures. A preconditioned conjugate gradient method is used in the algorithm with either a lumped or a Dirichlet preconditioner, and scalable convergence rates are proved. This framework is also used to describe several previously developed FETI-DP algorithms and greatly simplifies their analysis. Numerical experiments of solving a two-dimensional incompressible Stokes problem demonstrate the performances of the discussed FETI-DP algorithms represented under the same framework.