Information sheet ECTS Syllabus
Course syllabus D1-NADR - Numerical analysis of differential equations (FCE - 2020/2021 - post-graduate studies)
Slovak University of Technology in Bratislava
|Course unit code:|
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 - doctoral (semi-compulsory), 1. year
Level of study:
|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: 11
|Name of lecturer(s):|
31. 3. 2020
prof. RNDr. Karol Mikula, DrSc. and programme supervisor
Last modification made by Ing. Marián Dubík on 03/31/2020.