This page provides several computational examples for eigenvalues evaluation, error constant estimation and so on. Such computation is needed in numerical analysis for solving partial differential equation with numerical methods.
Online computation
Library for interpolation error constants evaluation
- Code at GitHub: https://github.com/xfliu/constant_estimation/
Computation examples:
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Evaluate the eigenvalue of the Laplacian through Jupyter Notebook. (Last updated: 2019/12/15)
Download code at GitHub: https://github.com/xfliu/eigenvalue
Online live demo. GO (Supported by Binder.) After entering the new page by the link, it takes about 30 seconds to open a live demo.
- Interpolation error constants estimation [ GO ]
Example: Evaluation of Babuska-Aziz constant over triangle T
$$C = \sup_{v \in V(T)} \frac{\|\nabla v\|_0}{\|v\|_0}, \text{ where } V(T)=\{ v \in H^1(T) | \int_{e_1} v ds=0 \}\:. $$ - Evaluation of eigenvalues of Laplace operator on polygonal domain. [ GO ]
$$ -\Delta u = \lambda u \text{ in } \Omega, u=0\text{ on }\partial \Omega $$
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Orbit of a planet around sun. [ GO ]
Orbit computing - To be added. ...
Computation environment
All the computing are performed Google Cloud Platform, where Google Compute Engine service is used. The on-demand computing server is booted only when a computation task is requested from browsers by users.