Eigenvalue bounds for Laplacian




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

Bounding eigenvalue for the Laplacian by using the finite element method

Abstract of the project

This project shows how to apply the conforming and non-conforming FEMs to obtain explicit lower band upper bounds the eigenvalues of the Laplacian.

Code structure

There are two cases of numerical computation. In each case folder, there is the setting.ini file to configure the mesh size for FEM computation.

  • Unit square domain. The eigenvalue problem has a closed form and the estimated error bound is compared with the error itsself.
  • L-shaped domain. This code displays the etimated bound in case the eigenfunctions may not have $H^2$-regularity.

How to run the code

Open file Eigenvalue_Problem_Step_By_Step.ipynb and run the cells.

About the directory

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

Virtual Machine Setting


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About Machine Type

The machine with type as "n1-standard-1" has 1 CPU Core and 4GB memory. The Google app compute engine provides a detailed guide of the machine type. For more detailed information, please refer to More detail.
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