Analysis of Iterative Methods for the Steady and Unsteady Stokes Problem: Application to Spectral Element Discretizations

Creators: Maday, Yvon; Meiron, Dan; Patera, Anthony T.; Rønquist, Einar M.

Abstract

A new and detailed analysis of the basic Uzawa algorithm for decoupling of the pressure and the velocity in the steady and unsteady Stokes operator is presented. The paper focuses on the following new aspects: explicit construction of the Uzawa pressure-operator spectrum for a semiperiodic model problem; general relationship of the convergence rate of the Uzawa procedure to classical inf-sup discretization analysis; and application of the method to high-order variational discretization.

Additional Information

© 1993 Society for Industrial and Applied Mathematics. Received by the editors September 25, 1990; accepted for publication (in revised form) March 19, 1992. This work was supported by the Office of Naval Research and Defense Advanced Research Projects Agency contract N00014-89-J-1610, by Office of Naval Research contract N000114-88-K-0188, by National Science Foundation grant ASC-8806925, by Department of Energy Office of Energy Sciences grant DE-AS03-76ER-72012, Applied Mathematical Sciences (KC-07-01-01), and by Nektonics Research Corporation. We would like to thank Paul Fischer at Brown University, and Intel Scientific Computers for providing us with the parallel spectral element results.

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