18. 7. 2019  2:25 Kamila
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Sylabus predmetu D1-NADR - Numerical analysis of differential equations (FCE - 2018/2019 - post-graduate studies)


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University: Slovak University of Technology in Bratislava
Faculty: Faculty of Civil Engineering
Course unit code: D1-NADR
Course unit title: Numerical analysis of differential equations
Mode of delivery, planned learning activities and teaching methods:
workshop2 hours weekly / 26 hours per semester of study (on-site method)

 
Credits allocated: 5
 
Recommended semester/trimester: Applied Mathematics - doctoral (semi-compulsory), 1. year
Applied Mathematics (in english language) - doctoral (semi-compulsory), 1. year
Level of study: 3.
Prerequisites for registration: none
 
Assesment methods:
Correctly elaborated all the assignments, exam.
 
Learning outcomes of the course unit:
Deepening of knowledge from the theory of functional spaces. Obtaining of basic knowledge from numerical analysis of the finite element and finite volume method for elliptic and parabolic differential equations.
 
Course contents:
- Functional spaces Wk,p(Ω).
- Trace theorem from W1,2(Ω) into L2(Ω) and its generalization.
- Embedding theorems.
- The estimation of errors for the numerical solution of elliptic equations obtained by the finite element method.
- Lax - Milgram theorem and Cea lema.
- The finite volume method for solving an elliptic boundary value problem with homogeneous
Dirichlet boundary conditions, the discrete Poincare inequality.
- Rothe method for the heat equation, stability estimates, Gronwall's lemma, Arzela -Ascoli theorem and the convergence of Rothe's method.
- The basic idea of discretization of Perona-Malik equation by the finite volume method and proof of convergence of numerical solutions to the weak solution.
 
Recommended or required reading:
Basic:
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.

 
Language of instruction: slovak and english or english
 
Notes:
 
Courses evaluation:
Assessed students in total: 9

PN
100,0 %0 %
Name of lecturer(s): doc. RNDr. Angela Handlovičová, PhD. (examiner, instructor, lecturer) - slovak, english
prof. RNDr. Karol Mikula, DrSc. (examiner, instructor, lecturer, person responsible for course, tutor) - slovak, english
 
Last modification: 31. 10. 2017
Supervisor: prof. RNDr. Karol Mikula, DrSc. and programme supervisor


Last modification made by Ing. Peter Korčák on 10/31/2017.

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