18. 7. 2019  3:31 Kamila

Sylabus predmetu I1-NADR - Numerical analysis of differential equations (FCE - SS 2018/2019)

Informačný list          ECTS          Sylabus

Slovenčina          Angličtina

University: Slovak University of Technology in Bratislava
Faculty: Faculty of Civil Engineering
Course unit title: Numerical analysis of differential equations
Mode of delivery, planned learning activities and teaching methods:
 lecture 2 hours weekly (on-site method) seminar 2 hours weekly (on-site method)

Credits allocated: 5

Recommended semester/trimester: Mathematical and Computational Modeling - master (compulsory), 4. semester
Level of study: 2.
Prerequisites for registration: none

Assesment methods:
During the semester 2 successfully passed tests.
Obtaining at least 56 points from the final exam.

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.

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.

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.

Language of instruction: slovak or english

Notes:

Courses evaluation:
Assessed students in total: 21

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Name of lecturer(s): doc. RNDr. Angela Handlovičová, PhD. (examiner, instructor, lecturer, person responsible for course) - slovak, english

Last modification: 28. 2. 2019
Supervisor: doc. RNDr. Angela Handlovičová, PhD. and programme supervisor

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

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