Course detail

Numerical Methods III

FSI-SN3 Acad. year: 2026/2027 Winter semester

Supervisor

doc. Ing. Petr Tomášek, Ph.D.

Department

Institute of Mathematics

Learning outcomes of the course unit

Prerequisites

Differential and integral calculus for multivariable functions. Fundamentals of functional analysis. Partial differential equations. Numerical methods, especially interpolation, quadrature and solution of systems of ODE. Basic programming skills.

Planned learning activities and teaching methods

Assesment methods and criteria linked to learning outcomes

Language of instruction

Czech

Aims

Specification of controlled education, way of implementation and compensation for absences

The study programmes with the given course

Programme N-MAI-P: Mathematical Engineering, Master's
branch ---: no specialisation, 5 credits, compulsory

Programme C-AKR-P: , Lifelong learning
branch CZS: , 5 credits, elective

Type of course unit

 

Lecture

26 hours, optionally

Syllabus

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

13 hours, compulsory

Syllabus

Seminars will follow the lectures. Students work on assigned projects under the guidance of an instructor.