Theory and Computation for the Finite Element Method

Abstract

The finite element method (FEM) is a popular method for numerically solving (partial) differential equations arising in engineering and mathematical modeling. A domain of interest is represented as an assembly of finite elements. Approximating functions in finite elements are determined in terms of nodal values of a physical field which is sought. A continuous physical problem is transformed into a discretized finite element problem with unknown nodal values. For a linear problem, a system of linear algebraic equations should be solved. Function values inside finite elements can be recovered using nodal values. The key steps of this special lecture are outlined below.

Lectures

May 31(Sat)

1. Lecture 1. Introduction to Numerical Methods: Finite Difference, Finite Element, and Spectral Methods, 10:00 – 11:00
2. Lecture 2. Finite Element Approximation: Triangulation and Piecewise Polynomial Subspaces, 11:00 – 12:00
3. Lecture 3. Interpolation and Projection Operators in Finite Element Spaces, 14:00 – 15:00
4. Lecture 4. Variational Formulation and the Galerkin Method, 15:00 – 16:00
5. Lecture 5. Galerkin Approximation of Elliptic Problems: Formulation and Analysis, 16:00 – 17:00

June 1(Sun)

3. Lecture 6. Existence and Uniqueness of Galerkin Solutions, 10:00 – 11:00
4. Lecture 7. Introduction to Mixed Finite Element Methods, 11:00 – 12:00
5. Lecture 8. Least-Squares Mixed Methods for Elliptic and Stokes Equations, 14:00 – 15:00
6. Lecture 9. Mesh Refinement of Basic Triangulations, 15:00 – 16:00
7. Lecture 10. Assembling and Solving the Algebraic Linear System, 16:00 – 17:00

Venue

• #213, College of Natural Sciences, Kyungpook National University, Daegu, Korea

Hands-on Session

A hands-on session is planned during the lecture. Participants are encouraged to bring their own laptops. The programming language used for the hands-on session will be Python.

Accommodation Suggestion

• Hotel Inter-Burgo Exco (호텔 인터불고 엑스코)
• Standard double room rate is about KRW120,000 – KRW150,000 as of Feb. 2024.
• Breakfast is not included.
• Distance from Venue : 40min. by walk (map), 30min. by bus and walk

• Browndot-KNU (브라운도트-경북대점)
• Standard double room rate is about KRW80,000 – KRW100,000 as of Dec. 2023.
• Breakfast is not included.
• Distance from Venue : 15min. by walk (map)

Contact

• Byung Hee An (anbyhee_at_knu.ac.kr)
• Hayoung Choi (hayoung.choi_at_knu.ac.kr)

Sponsored by

• National Research Foundation of Korea (2022R1A5A1033624 and RS-2024-00342939)

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