Novel Approach for Solving the Discrete Stokes Problems Based on Augmented Lagrangian and Global Techniques with Applications for Stokes Problems

Abstract

In this paper, a novel augmented Lagrangian preconditioner based on the global Arnoldi for accelerating the convergence of Krylov subspace methods is applied to linear systems of equations with a block three-by-three structure, and these systems typically arise from discretizing the Stokes equations using mixed finite-element methods. Spectral analyses are established for the exact versions of these preconditioners. Finally, the obtained numerical results claim that our novel approach is more efficient and robust for solving the discrete Stokes problems. The efficiency of our new approach is evaluated by measuring the computational time.

Keywords

Stokes equation / Saddle point problem / Krylov subspace method / Global Krylov subspace method / Augmented Lagrangian-based preconditioning

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Shanghai University