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

Maday, Yvon

Meiron, Dan

Patera, Anthony T.

Rønquist, Einar M.

English

Caltech Authors - Main

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

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 discretiz-ation analysis; and application of the method to high-order variational discretization

Yvon Maday

Anthony T. Patera

Einar

M. Ronquist

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

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