Chebyshev pseudospectral solution of the Stokes equations using finite element preconditioning. (English) Zbl 0672.76039
Summary: The Stokes equations are solved by a Chebyshev pseudospectral method on a rectangular domain. As the resulting system of algebraic equations is very difficult to factorize, a preconditioning is designed using a finite element technique. The FEM solver constitutes the masterpiece of a Richardson iteration process. Several finite elements are investigated: the 9-nodes Lagrangian element Q2-Q1, the Q1-Q0 element, and the Q1-Q1 element. An eigenvalue analysis is carried out in order to pinpoint the characteristic features of each preconditioner. It is shown that the Q2- Q1 element yields the best convergence results. The power of this choice is demonstrated on theoretical solutions and on the regularized square cavity problem.
MSC:
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
Keywords:
Stokes equations; Chebyshev pseudospectral method; rectangular domain; Richardson iteration process; finite elements; Lagrangian element; eigenvalue analysis; preconditioner; regularized square cavity problemReferences:
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