Information sheet ECTS Syllabus
Course syllabus I1-NADR - Numerical analysis of differential equations (FCE - SS 2019/2020)
|University:||Slovak University of Technology in Bratislava|
|Faculty:||Faculty of Civil Engineering|
|Course unit code:||I1-NADR|
|Course unit title:||Numerical analysis of differential equations|
|Mode of delivery, planned learning activities and teaching methods:|
|Recommended semester/trimester:||Mathematical and Computational Modeling - master (compulsory), 4. semester|
|Level of study:||2.|
|Prerequisites for registration:||none|
|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.|
|- 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:|
|Language of instruction:||slovak or english|
|Assessed students in total: 21|
|Name of lecturer(s):||doc. RNDr. Angela Handlovičová, PhD. (examiner, instructor, lecturer, person responsible for course) - slovak, english|
|Last modification:||16. 4. 2019|
|Supervisor:||doc. RNDr. Angela Handlovičová, PhD. and programme supervisor|
Last modification made by Ing. Peter Korčák on 04/16/2019.