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Inf-Sup and Condition Number of the Penalty Method for Stokes Problem

F. Z. Nouri


The aim of this work is to evaluate the dependence of the condition number on the constant which appears in the standard inf-sup condition for the divergence operator.The penalty method when applied to the Stokes problem provides a very ecient 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 discretization of the Stokes problem, we prove a posteriori estimates that allow us to optimize both the penalty parameter and the condition number as functions of the discretization parameter. Numerical experiments confirm the interest of such an algorithm with optimal or non-optimal inf sup constants.


Penalty Method, Stokes Problem, Inf-Sup and Condition Number

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