, Volume 58, Issue 1, pp 203-214

The conditioning of the stiffness matrix for certain elements approximating the incompressibility condition in fluid dynamics

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Summary

In order to solve the Stokes equations numerically, Crouzeix and Raviart introduced elements satisfying a discrete divergence condition. For the two dimensional case and uniform triangulations it is shown, that using the standard basis functions, the conditioning of the stiffness matrix is of orderN 2, whereN is the dimension of the corresponding finite element space. Hierarchical bases are introduced which give a condition number of orderN log(N)3.