Multilevel Solvers of First-Order System Least-Squares

                             for Stokes Equations

                               Chen-Yao G.  Lai
                            cylai@math.ccu.edu.tw
                          Department of Mathematics
                       National Chung Cheng University
                          No. 160, San-Hsing Village
                           Ming-Hsiung, Chia-Yi 621
                                    Taiwan

Recently, The use of first-order system least squares principle for the
approximate solution of Stokes problems has been extensively studied by Cai,
Manteuffel, and McCormick [1,2].  In this paper, we study multilevel solvers
of first-order system least-squares method for the generalized Stokes
equations based on the velocity-vorticity-pressure formulation in three
dimensions.  The least-squares functionals is defined to be the sum of the
$L^2$-norms of the residuals, which is weighted appropriately by the Reynolds
number.  We develop convergence analysis for additive and multiplicative
multilevel methods applied to the resulting discrete equations.


References: 

1. Z. Cai, T. Manteuffel, and S. McCormick. First-order system least
  squares for the stokes equations, with application to linear elasticity, 
  SIAM J. Numer. Anal. (submitted).

2. Z. Cai, T. Manteuffel, and S. McCormick. First-order system least
  squares for velocity-vorticity-pressure form of the stokes equations, 
  with application to linear elasticity, The Seventh Copper Mountain 
  Conference on Multigrid Methods.