Numerical Solution of Partial Differential Equations with Finite Element Method

Garant předmětu:

Petr Sváček

Lecturer:

Petr Sváček

Tutor:

Petr Sváček

Supervisor:

Department of Technical Mathematics

Synopsis:

Variational formulation of boundary value problems of partial differential equations, weak formulation, mathematical background of finite element method.

Weak and classical solutions.

A priori error estimate.

A construction of the finite element space.

Application of finite element method for elliptic, parabolic and hyperbolic partial differential equations.

Problems in 1D, 2D.

Application of the finite element method for heat conduction, wave equation, convection-diffusion problems, Stokes problem and Navier-Stokes equations.

Requirements:

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

Sváček, P., Feistauer, M.: Metoda konečných prvků, 2006, Vydavatelství ČVUT.

Johnson, C.: Numerical Solution of Partial Differential Equation by the Finite Element Method, 1987, Cambridge University Press.

P. G. Ciarlet, The Finite Element Method for Elliptic Problems, SIAM, 2002 (2nd edition).

Míka, S., Přikryl, P.: Numerické metody řešení parciálních diferenciálních rovnic, 1995, ZČU Plzeň.

Vitásek, E.: Numerické metody, 1987, SNTL.

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: