Implementation of a least-squares finite element method for solving the Stokes problem with a parameter

Abstract

The implementation of a least-squares finite element method for solving the generalized stationary Stokes problem (i.e. the Stokes problem with an additional term α u in the motion equation, where α is a big parameter and u is the velocity vector function) is considered. The basis of this method is the reduction of the second-order boundary value problem to a system of first-order partial differential equations and the minimization of the residuals of these equations in some finite element space by the least-squares method. The main advantage of this approach consists in the fact that the same approximating space is used for both the velocity and the pressure. The condition number of the resulting system of linear algebraic equations depends on the big parameter α; an efficient preconditioner for this system is constructed. Copyright © 1999 John Wiley & Sons, Ltd.