Stabilization of the finite element method for the stationary Stokes problem for an incompressible fluid

Abstract

The solution of the stationary Stokes problem through the finite element method using linear elements leads to instabilities in the obtained solution. There are two sources of difficulties to solve numerically this problem. The first one is related to the incompressibility condition and the second one relies in the analysis of the behavior of a bulid with high viscosity. This work is devoted to the analysis, and implementation in a Matlab code, of the Galerkin Least-Squares stabilization of the finite element solution when linear elements are used