Rqn. Zhou, PRECONDITIONED FINITE-ELEMENT ALGORITHMS FOR 3D STOKES FLOWS, International journal for numerical methods in fluids, 17(8), 1993, pp. 667-685
Preconditioned conjugate gradient algorithms for solving 3D Stokes pro
blems by stable piecewise discontinuous pressure finite elements are p
resented. The emphasis is on the preconditioning schemes and their num
erical implementation for use with Hermitian based discontinuous press
ure elements. For the piecewise constant discontinuous pressure elemen
ts, a variant implementation of the preconditioner proposed by Cahouet
and Chabard for the continuous pressure elements is employed. For the
piecewise linear discontinuous pressure elements, a new preconditione
r is presented. Numerical examples are presented for the cubic lid-dri
ven cavity problem with two representative elements, i.e. the Q2-P0 an
d the Q2-P1 brick elements. Numerical results show that the preconditi
oning schemes are very effective in reducing the number of pressure it
erations at very reasonable costs. It is also shown that they are inse
nsitive to the mesh Reynolds number except for nearly steady flows (Re
(m) --> 0) and are almost independent of mesh sizes. It is demonstrate
d that the schemes perform reasonably well on non-uniform meshes.