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 code:||I1-NADR|
|Course unit title:||Numerical analysis of differential equations|
|Mode of completion and Number of ECTS credits:||Classified fulfillment of requirements (5 credits)|
|- 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.
Last modification made by Ing. Peter Korčák on 02/28/2019.