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.