On improvement of convergence rate for a certain method of solving the Stokes problem (Q1842491)

The general theory of iterative algorithms for problems with saddle operators is applied to the classical Stokes problem. After reformulating the original problem as an equivalent problem containing two arbitrary parameters \(\alpha\) and \(\beta\), the author investigates the corresponding iterative procedure using spectral properties of operator pencil of elasticity theory. This enables one to find optimal values for \(\alpha\) and \(\beta\) providing an essentially improved convergence of the procedure. To confirm the above results, some numerical experiments are reported for finite difference approximation of the considered problem in a model domain -- the unit square.