The eigenvalue estimation for Stokes operator.



  • DEMO

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.

About the directory

Folders or files beginning with a dot are not displayed by default.

Virtual Machine Setting

(Please login first to start the virtual machine.)

About file revision at virtual machine

For owner of the project, the file revised on the virtual machine will be saved after shutting down the server. As a visitor user, one can revise files in the booted virtual machine, but the revision will be aborted once the server is shut down.

About Machine Type

The Google app compute engine provides a detailed guide of the machine type. For more detailed information, please refer to More detail.
If you need a high-spec machine type, please contact the site manager.