# Course syllabus I1-NADR - Numerical analysis of differential equations (FCE - SS 2018/2019)

**ECTS**Syllabus

Slovak

**English**

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: | |||||||

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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.*