Title

Author

xfliu

Description

The eigenvalue estimation for Stokes operator.

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Stokes eigenvalue problem

We apply the conforming FEM and the non-conforming FEM to solve the Stokes eigenvalue problems on 2D and 3D domains.

Eigenvalue problem in $R^d$ domain:

Let $V:={v\in H_0^1(\Omega)^d\:|\: \mbox{div } v=0 }$. Find $u\in V$ and $\lambda\in R$ such that

$$ (\nabla u, \nabla v) = \lambda (u,v)\quad \forall v\in V\:. $$

In this notebook both the conforming and non-conforming FEMs are used to obtain the upper and lower bounds, respectively.

If the projection error constant for conforming FEM is available (which is to be evaluated by other algorithm and skipped here), one can further use the projection error constant to get the lower eigenvalue bounds directly.

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