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Course, academic year 2023/2024
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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 2021
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: yes / unlimited
Key competences: 4EU+ Flagship 3
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. Mgr. Petr Knobloch, Dr., DSc.
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
Annotation -
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.
Last update: T_KNM (28.04.2015)
Course completion requirements -

Credit is not required for the exam.

Credit will be given for successful solutions of at least 50 % homeworks which will be given to the students regularly during the semester. The solutions of the homeworks have to be submitted via SIS till the deadlines. If a student will not acquire the credit for solutions of homeworks, the credit can be obtained for a successful written test (at least 50% points). The credit test can be repeated twice.

Last update: Knobloch Petr, doc. Mgr., Dr., DSc. (10.10.2020)
Literature -

V. Dolejší, P. Knobloch, V. Kučera, M. Vlasák: Finite element methods: Theory, applications and implementations, Matfyzpress, Praha, 2013

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, 2008

A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements, Springer-Verlag, New York, 2004

Last update: Knobloch Petr, doc. Mgr., Dr., DSc. (11.10.2017)
Requirements to the exam -

The exam is oral.

The requirements for the exam correspond to the syllabus of the subject in the extent that was presented at the lecture.

Last update: Kučera Václav, doc. RNDr., Ph.D. (29.10.2019)
Syllabus -

abstract variational problem, Lax-Milgram lemma;

Galerkin approximation, Cea's lemma;

Lagrange and Hermite finite elements, concept of affine equivalence;

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 Galerkin approximations in the energy and L2 norm;

numerical integration in FEM, errors of quadrature formulas;

error of finite element approximation in the presence of numerical integration;

FEM for parabolic problems

Last update: Knobloch Petr, doc. Mgr., Dr., DSc. (07.09.2020)
Entry requirements -

Classical theory of partial differential equations of the 2nd order, basics of functional analysis.

Last update: Haslinger Jaroslav, prof. RNDr., DrSc. (12.05.2019)
 
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