camtips/blog/research/Basics-of-Finite-Elements/

[giscus[bot]]

camtips/blog/research/Basics-of-Finite-Elements/

https://lyc102.github.io/camtips/blog/research/Basics-of-Finite-Elements/

[scaomath]

In $\mathbb{R}^n$, $P_k(\mathbb{R}^n) = \{\text{polynomials of maximum total degree } k \text{ in } x_1,...,x_n\}$, and its element can be written as $p(x) = \sum_{|\alpha| \leq k} a_{\alpha} x^{\alpha}$ where $\alpha = (\alpha_1, \alpha_2, \dots, \alpha_n)$ is a multi-index. Thus, the polynomial space's dimension is equal to how many ways to choose $\alpha$. Equivalently, it is like putting $n$ bars to separate $n+k+1$ balls into $n+1$ parts, there should be at least one ball between different bars, which gives us ${n+k \choose n}$.

[lihua64]

写书的时候，老师您可以试一下Elegant LaTeX模板吗？

[lyc102]

好的，我去查一下这个模版，试用一下。

[lihua64]

感谢老师(✪▽✪)的无私付出，我之前看过东南大学的李逸老师拿这个写书

[FL-CFD]

Thanks for this useful notes. I wonder how did you plot the plots in Lagrange elements in 3D?

[FL-CFD]

Yes. How did you plot the green elements and black spheres?

[lihua64]

嗯嗯，我觉得blender这个软件应该可以做，或者一些关于CAD的轻量级的开源软件，提供Python和Qt接口。
如果是一些简单的流程图，excalidraw可能有用。
因为我对CAD软件不怎么了解，所以可能无法给您有用的建议。

[FL-CFD]

Thank you very much. Will take a look.

[lihua64]

您客气了，希望有帮助，欢迎您的使用体验分享

[lyc102]

我自己写的MATLAB 软件。下载 ifem，然后查找 lattice3.m

[lyc102]

插图一般是用 ifem 来画的。可以在 https://lyc102.github.io/ifem 下载软件。查找 lattice.m or lattice3.m 来学习如何画拉格朗日元的插值点。

[FL-CFD]

Thank you. Will take a look. But just curious that is there any plan to translate the ifem into python? Many people don't have Matlab license. Although matlab online is relatively free, but it is not very convenient.

[lyc102]

My student Huayi Wei has developed such a software package https://github.com/weihuayi/fealpy

[FL-CFD]

Thank you very much, Prof. Chen. Will take a look!