Communications of the
Korean Mathematical Society CKMS

Multigrid methods for two first-order system least squar- es (FOSLS) using bilinear finite elements are developed for the pure traction problem of planar linear elasticity. They are {\it two-stage} algorithms that first solve for the gradients of displacement, then for the displacement itself. In this paper, concentration is given on solving for the gradients of displacement only. Numerical results show that the convergences are uniform even as the material becomes nearly incompressible. Computations for convergence rates are included.

Keywords: First-order system least squares, Lam\'{e} constants, multigrid method, pure traction problem

MSC numbers: 65F10, 65N55, 73K10