Information sheet ECTS Syllabus
Course syllabus I1-NADR - Numerical analysis of differential equations (FCE - SS 2018/2019)
|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|
|- 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:|
|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.