Jul 22, 2019   12:11 p.m. Magdaléna
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Course syllabus I1-NADR - Numerical analysis of differential equations (FCE - SS 2018/2019)

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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)
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.

Last modification made by Ing. Peter Korčák on 02/28/2019.

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