LEAST-SQUARES FINITE-ELEMENT METHOD FOR THE STOKES PROBLEM WITH ZERO RESIDUAL OF MASS CONSERVATION

In this paper the simulation of incompressible flow in two dimensions by the least-squares finite element method (LSFEM) in the vorticity-ve locity-pressure version is studied. In the LSFEM, the equations for co ntinuity of mass and momentum and a vorticity equation are minimized o n a discretization of the domain of interest. A problem is these equat ions are minimized in a global sense. Thus this method may not enforce that div (u) under bar = 0 at every point of the discretization. In t his paper a modified LSFEM is developed which enforces near zero resid ual of mass conservation, i.e., div (u) under bar is nearly zero at ev ery point of the discretization. This is accomplished by adding an ext ra restriction in the divergence-free equation through the Lagrange mu ltiplier strategy. In this numerical method the inf-sup or say LBB con dition is not necessary, and the matrix resulting from applying the me thod on a discretization is symmetric; the uniqueness of the solution and the application of the conjugate gradient method are also valid. N umerical experience is given in simulating the flow of a cylinder with diameter 1 moving in a narrow channel of width 1.5. Results obtained by the LSFEM show that mass is created or destroyed at different point s in the interior of discretization. The results obtained by the modif ied LSFEM show the mass is nearly conserved everywhere.