A mass conservative least-squares finite element method for the Stokes problem

In the paper the simulation of incompressible flow in 2D by the least-squares finite element method (LSFEM) in the velocity-vorticity-pressure version is studied. A problem with this method is that it does not conserve mass exactly, i.e. div u(h) not equal 0 exactly. In the paper a modified LSFEM is developed which enforces a near zero residual of mass conservation, i.e. div u is nearly zero at every point of the discretization. This is accomplished by adding an extra restriction in the divergence free equation through the Lagrange multiplier strategy.