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Finite Element Method - NNUM015

Title:	Metoda konečných prvků
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. Mgr. Petr Knobloch, Dr., DSc.
Classification:	Mathematics > Numerical Analysis
Incompatibility :	NMNV405, NNUM002
Interchangeability :	NMNV405, NNUM002
Is incompatible with:	NNUM002, NMNV405
Is interchangeable with:	NNUM002, NMNV405

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KNM (19.05.2008)

Mathematical foundations of the finite element method for the numerical solution of partial differential equations.

Aim of the course -

Last update: T_KNM (16.05.2008)

The course gives students a knowledge of mathematical basics of the finite element method.

Literature - Czech

Last update: T_KNM (16.05.2008)

Brenner S.,Scott R.: The mathematical theory of finite element methods, 1994

Ciarlet, P.G.: The finite element method for elliptic problems, l978

Haslinger J.: Metoda konečných prvků, skripta MFF UK

Thomée V.: Galerkin finite element methods for parabolic problems, 1997

Teaching methods -

Last update: T_KNM (16.05.2008)

Lectures and tutorials in a lecture hall.

Requirements to the exam -

Last update: T_KNM (16.05.2008)

Examination according to the syllabus.

Syllabus -

Last update: T_KNM (16.05.2008)

Short introduction to Sobolev spaces, basic ideas of the finite element method, abstract variational problem, Lax-Milgram lemma, triangulations of the computational domain.

Examples of finite elements defined on simplices, rectangles and hexahedra.

Affine equivalence of finite elements, concept of a reference finite element, general definition of finite element spaces.

Interpolation in Sobolev spaces.

Approximation properties of finite element spaces.

Convergence of discrete solutions of elliptic problems.

Numerical integration, First Strang's lemma, Bramble-Hilbert lemma.

Error estimates for finite element discretizations of elliptic problems in the presence of numerical integration.

Further variational crimes: nonconforming and isoparametric finite elements, approximation of the boundary.

Finite element discretization of parabolic problems: error estimates for a semidiscretization in space and for the fully discretized problem.

Entry requirements -

Last update: T_KNM (16.05.2008)

Students are expected to have attended a basic course of functional analysis and to have attended or to attend a course on the modern theory of partial differential equations, e.g., NDIR045.