Krylov-Based Uzawa Algorithms for the Solution of the Stokes Equations Using Discontinuous-Pressure Tetrahedral Finite Elements

The objective of this work is to develop an efficient and robust Krylov-based Uzawa algorithm for the solution of the 3D steady-state and unsteady-state Stokes equations with discontinuous-pressure tetrahedral finite elements. To this end, a class of preconditioned conjugate gradient Uzawa algorithms are presented and compared to those of the literature for other finite element types. A comparison is also made with an inexact Uzawa algorithm for the steady-state case. An analysis of the results obtained for various problems leads to an iterative scheme that is well adapted to the solution of Stokes problems of all sizes and complexities such as those found in industrial applications.