H least-squares method for the velocity–pressure–stress formulation of Stokes equations

This paper studies the discrete H⁻¹-norm least-squares method for the incompressible Stokes equations based on the velocity–pressure–stress formulation by the least-squares functional defined as the sum of L²-norms and H⁻¹-norm of the residual equations. Some computational experiments by multigrid method and preconditioning conjugate gradient method (PCGM) on this method are shown by taking efficient and β in the discrete solution operator T_h=h²I+βB_h corresponding to the minus one norm. We also propose a new method and compare it with PCGM and multigrid method through the analysis of numerical experiments depending on the choice of β.