Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Finite Element Method 1 - NMNV405

Title:	Metoda konečných prvků 1
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2016
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Jaroslav Haslinger, DrSc.
Class:	M Mgr. MA M Mgr. MA > Povinně volitelné M Mgr. MOD M Mgr. MOD > Povinné M Mgr. NVM M Mgr. NVM > Povinné
Classification:	Mathematics > Differential Equations, Potential Theory, Numerical Analysis
Comes under:	Doporučené přednášky 2/2
Incompatibility :	NNUM002, NNUM015
Interchangeability :	NNUM002, NNUM015
Is incompatible with:	NNUM015, NNUM002
Is interchangeable with:	NNUM015, NNUM002

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KNM (28.04.2015)

The aim of this course is to present the mathematical theory of finite element methods and their applications in solving linear elliptic equations. This covers: approximation theory for mappings preserving polynomials , application to the Lagrange and Hermite interpolation of functions in multidimensional space , description of the most frequently used finite elements, the error analysis, numerical integration in FEM.

Literature

Last update: doc. Mgr. Petr Knobloch, Dr., DSc. (11.10.2017)

J. Haslinger: Metoda konečných prvků pro řešení variačních rovnic a nerovnic eliptického typu, skripta, Praha 1980

P.G. Ciarlet: The Finite Element Method for Elliptic Problems, Studies in Mathematics and its Applications 4, North Holland Publishing Company, Amsterdam, 1978

S.C. Brenner, L.R.Scott: The Mathematical Theory of Finite Element Methods, Text in Applied Mathematics 15, Springer-Verlag, 1994

Syllabus -

Last update: doc. Mgr. Petr Knobloch, Dr., DSc. (11.10.2017)

Abstract linear elliptic equations, Lax-Milgram theorem;

Ritz-Galerkin approximation, Cea's lemma;

Lagrange and Hermite finite elements,examples, concept of affine equaivalence;

Construction of finite element spaces, satisfaction of stable boundary conditions;

Approximation theory in Sobolev spaces, application to Lagrange and Hermite interpolation of functions;

Error estimates for Ritz-Galerkin approximations in the energy and L2- norm.

Numerical integration in FEM, errors of quadrature formulas, error of full finite element approximation in the presence of numerical integration

Special topics: mixed finite element approximations, Babuska-Brezzi condition, applications in flow problems