The explicit lower bound and upper bound for the Laplace differential operator are obtained by using the conforming and non-conforming finite element method.



  • DEMO


For the eigenvalue problem of the Laplacian, the conforming and non-conforming finite element methods are utilized to provide explicit upper and lower bounds for the eigenvalues.

Particularly, by applying Liu's method, the lower eigenvalue bounds can be easily obtained through the Crouzeix-Rarviart finite element method; such a method even works for non-convex domains.

For both Dirichlet and Neumann eigenvalues problems over the unit square domain and an L-shaped domain, the explicit eigenvalue bounds are provided.

  • Dirichlet eigenvalues

  • Neumann eigenvalues

How to run it

Start the demo server in the demo page, then run the code through JupyterLab interface.


Online live demo at Ganjin.online.

URL: https://www.ganjin.online/project/EigenvalueBound

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