Jul 18, 2019   9:13 p.m. Kamila
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Course syllabus I1-NADR - Numerical analysis of differential equations (FCE - SS 2018/2019)


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University: Slovak University of Technology in Bratislava
Faculty: Faculty of Civil Engineering
Course unit title: Numerical analysis of differential equations
Course unit code: I1-NADR
Mode of completion and Number of ECTS credits: Classified fulfillment of requirements (5 credits)
 
Name of lecturer: doc. RNDr. Angela Handlovičová, PhD. (examiner, instructor, lecturer, person responsible for course) - slovak, english
 
Learning outcomes of the course unit:
Profounding the knowledge of functional spaces theory. Basic knowledge of numerical analysis theory for elliptic and parabolic PDE's.
 
Prerequisites and co-requisites: none
 
Course contents:
- Functional spaces Lp(Ω).
- Functional spaces Wk,p(Ω).
- Trace theorem from W1,2(Ω) to L2 (Ω) and its generalization.
- Embedding theorems.
- Numerical solution of boundary value problems via Ritz-Galerkin method. Error estimates obtained by finite elemnt method in 1D for linear finite elements.
- Lax-Milgram theorem and Céa lemma.
- Finite volume method for the solution of elliptic boundary value problem for homogeneous Dirichlet boundary conditions. Discrete Poincare inequality.
- Rothe's method for heat equation, stability estimations, Gronwall lemma, Arzela - Ascoli theorem and convergence of Rothe's method.
- Basic ideas for the discretization of Perona-Malik equation by FVM. Convergence proof.
 
Recommended or required reading:
Basic:
REKTORYS, K. Variační metódy v inženýrskych problémech a v problémech matematické fyziky. Praha : SNTL, 1974. 600 p.
KUFNER, A. -- JOHN, O. -- FUČÍK, S. Function Spaces. Praha : ČSAV, 1977. 454 p.
BRENNER, S C. -- SCOTT, L. The mathematical theory of finite element methods. New York : Springer Verlag, 2002. 361 p. ISBN 0-387-95451-1.
MIKULA, K. -- RAMAROSY, N. Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing. Numerische Mathematik, 89. p. 561--590.

 
Planned learning activities and teaching methods: Lecture, seminar
2/2 - 48 hours per semester (on-site method)
 
Assesment methods and criteria: graded credit
 
Language of instruction: Slovak, English
 
Work placement(s): There is no compulsory work placement in the course unit.


Last modification made by Ing. Peter Korčák on 02/28/2019.

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