CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Finite Element Method

Code Completion Credits Range Language
01MKP ZK 3 1P+1C Czech
Garant předmětu:
Michal Beneš
Lecturer:
Michal Beneš
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

The course is devoted to the mathematical theory of the finite element method numerically solving boundary-value and initial-boundary-value problems for partial differential equations. Mathematical properties of the method are explained. The approximation error estimates are derived.

Requirements:

Basic course of Calculus, Linear Algebra and Numerical Mathematics, variational methods (in the extent of the courses 01MA1, 01MAA2-4, 01LA1, 01LAA, NM, or 01MA1, 01MAB2-4, 01LA1, 01LAB2, NMET, VAME held at the FNSPE CTU in Prague).

Syllabus of lectures:

1. Weak solution of boundary-value problem for an elliptic partial differential equation.

2. Galerkin method

3. Basics and features of the FEM

4. Definition and common types of finite elements.

5. Averaged Taylor polynomial

6. Local and global interpolant

7. Bramble-Hilbert lemma

8. Global interpolation error

9. Mathematical features of the FEM and details of use

10. Examples of software packages based on FEM

Syllabus of tutorials:

Exercise is merged with the lecture and contains examples of problem formulation, examples on function bases, examples related to the interpolation theory and examples of software packages based on FEM, in particular.

Study Objective:

Knowledge:

Weak formulation of boundary-value and initial-boundary-value problems for partial differential equations, Galerkin method, basics of FEM, error estimates, applications.

Skills:

Formulation of given problem into the form convenient for FEM, method implementation, application, explanation of results and error assessment.

Study materials:

Key references:

[1] S. C. Brenner a L. Ridgway Scott, The mathematical theory of finite element methods, New York, Springer 1994

[2] P.G. Ciarlet, The finite element method for elliptic problems, Amsterdam, North-Holland, 1978

[3] V. Thomée, The Galerkin finite element methods for parabolic problems, LNM 1054, Berlin, Springer, 1984

[4] S. A. Ragab, H. E. Fayed, Introduction to Finite Element Analysis for Engineers, CRC Press, Taylor Francis, 2017

Recommended references:

[5] P. Grisvard, Elliptic problems in non-smooth domains, Boston, Pitman, 1985

[6] K. Rektorys, Variational methods in engineering and mathematical physics, Praha, Academia 1999 (translated to English)

Media and tools:

Computer training room with OS Windows/Linux and software package FEM

Note:
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-08-12
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