H−1 least-squares method for the velocity–pressure–stress formulation of Stokes equations Original Research Article

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 α and β in the discrete solution operator Th=αh2I+βBh 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.