Ⓜ️ Mimetic Spectral Element Method

The mimetic spectral element method is a novel method for solving partial differential equations (PDEs) numerically. It is of an arbitrary oder and fits both orthogonal and curvilinear meshes. It can be classified into the family of mixed finite element methods which is the one of the most important branches of finite element methods.

⛳️ Goals

During the lectures, we will introduce the basic ideas behind the method and focus on technical aspects of the method. In particular, we strengthen the practice; you will code your own library of all fundamental functionalities for finite element analysis in Python. By doing so, you will be able to understand all basic aspects of the mimetic spectral element method, and, therefore, to understand mixed finite element methods or any finite element method. In summary, the goals are

• Understand the mimetic spectral element method

• Understand mixed finite element methods

• Understand finite element methods

• Know how to program a finite element method code

Note that you will need to program in Python. If you do not know how to program in Python, it is a good opportunity to learn it. It is the easiest and most useful programming language. It is definitely something worth learning.

✒️ Assignments

The clue of the lectures will be the assignments. They will be clarified during the lectures. The assignments are

• A#0 — Lagrange/edge polynomials: Reduction and reconstruction

• A#1 — From one dimension to higher dimensions

• A#2 — From the reference element to physical elements

• A#3 — Numerical integration

• A#4 — Weak formulation and discretization: Single element

• A#5 — Weak formulation and discretization: Multiple elements

• A#6 — Error analysis

In these assignments, introductions and particular programing tasks are given. Your job is simple: 1) read the introductions, 2) program and test your Python codes.

You may need the help of following functions to finish the assignments:

• Gauss_Lobatto_nodes.py

📑 Report

After having done all the assignments, you need to assemble your answers into a final report. Note that it is not like put all your answers in a folder and zip it, or copy-paste all answers into one document. You need to use your answers as ingredients and to write one complete story in an report like an article. Your score will depend on this report. Note that you may be asked to do an oral exam to check whether the answers and the report are truly made by yourself.

For an instruction of the report, see Final_report.pdf.

📨 Contacts

• 张仪

• zhangyi_aero@hotmail.com

• 花江慧谷#4号楼，数学与计算科学学院，408A

• 你也可以通过填写 MESSAGE FORM 直接联系我

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