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.
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
Eigenvalue_Problem_Step_By_Step.ipynb and run the cells.
About the directory
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