Numerical Methods III (FSI-SN3)

Academic year 2025/2026
Supervisor: doc. Ing. Petr Tomášek, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
 
Learning outcomes and competences:
 
Prerequisites:
 
Course contents:
 
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:

Course-unit credit is awarded on the following conditions: elaboration of assignments.

The exam is oral. Its aim is to verify the student's theoretical knowledge and his/her ability to apply the acquired knowledge independently.
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 1 hrs. compulsory                  
Course curriculum:
    Lecture

The Finite Element Method in 1D:



  • Variational Formulation

  • Finite Element Approximation

  • Derivation of a Linear System of Equations

  • Computer Implementation

  • Galerkin Orthogonality, Best Approximation Property

  • A Priori Error Estimate

  • A Posteriori Error Estimate & Adaptive Finite Element Methods


The Finite Element Method in 2D:



  • Variational Formulation

  • Finite Element Approximation

  • Derivation of a Linear System of Equations

  • The Isoparametric Mapping

  • Different Types of Finite Elements

  • Computer Implementation (Data Structuring, Mesh Generation)


The Eigenvalue problems


Time-Dependant Problems
    Computer-assisted exercise

Seminars will follow the lectures. Students work on assigned projects under the guidance of an instructor.
Literature - fundamental:
1. M. G. Larson, F. Bengzon: The Finite Element Method: Theory, Implementation, and Applications, Springer, 2013.
2. K. Eriksson, D. Estep, P. Hansbo, C. Johnson: Computational Differential Equations, Cambridge University Press, 1996.
3.

M. S. Gockenbach: Understanding and implementing the finite element method. Philadelphia: Society for Industrial and Applied Mathematics, 2006.
4. A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements, Springer Series in Applied Mathematical Sciences, Vol. 159 (2004) 530 p., Springer-Verlag, New York
5. L. Čermák: Algoritmy metody konečných prvků, [on-line], available from: http://mathonline.fme.vutbr.cz/Numericke-metody-III/sc-1151-sr-1-a-142/default.aspx.
6.

A. Ženíšek: Matematické základy metody konečných prvků, [on-line], available from: http://mathonline.fme.vutbr.cz/Numericke-metody-III/sc-1151-sr-1-a-142/default.aspx.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
N-MAI-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory 2 1 W