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A penalty algorithm for the spectral element discretization of the Stokes problem. (English) Zbl 1267.76023

Summary: The penalty method when applied to the Stokes problem provides a very efficient algorithm for solving any discretization of this problem since it gives rise to a system of two equations where the unknowns are uncoupled. For a spectral or spectral element discretization of the Stokes problem, we prove a posteriori estimates that allow us to optimize the penalty parameter as a function of the discretization parameter. Numerical experiments confirm the interest of this technique.

MSC:

76D07 Stokes and related (Oseen, etc.) flows
76M22 Spectral methods applied to problems in fluid mechanics
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