Information sheet ECTS Syllabus
Course syllabus D1-NADR - Numerical analysis of differential equations (FCE - 2019/2020 - post-graduate studies)
|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:|
|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|
|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.|
|- 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:|
|Language of instruction:||slovak and english or english|
|Assessed students in total: 10|
|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.