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The course deals with various theoretical and practical aspects of the numerical solution of evolutionary differential
equations. We proceed from purely theoretic (Rothe method) to completely practical topics (discretization of
problems in time dependent domains). The course thus represents more of an overview of various techniques
connected to the numerical solution of evolutionary equations than one compact theory.
Last update: T_KNM (11.05.2015)
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The exam is oral. The examination requirements are given by the topics in the syllabus, in the extent to which they they were taught in course. Last update: Kučera Václav, doc. RNDr., Ph.D. (10.06.2019)
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REKTORYS K. Metoda časové diskretizace a parciální diferenciální rovnice, Teoretická knižnice inženýra, SNTL, Praha 1985
THOMÉE V. Galerkin finite element methods for parabolic problems, vol. 25, Springer-Verlag, Berlin Heidelberg, 2006.
HUNDSDORFER W., VERWER J.G.Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer Series in Comput. Math. 33, Springer, 2003 Last update: Kučera Václav, doc. RNDr., Ph.D. (29.10.2019)
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The exam is in oral form. The requirements are given by the scope covered in the lecture. Last update: Kučera Václav, doc. RNDr., Ph.D. (28.02.2018)
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Rothe method for parabolic problems. Existence and regularity of solutions, discretization error of the Rothe method.
Higher order discretizations of time derivatives, discontinuous Galerkin method in time. Discretization of hyperbolic problems.
Nonstationary advection and convection problems: Gibbs phenomenon, stabilization by artificial diffusion, semi-Lagrangian methods.
Evolutionary problems on time-dependent domains: ALE method, level set methods. Last update: KUCERA4 (20.09.2013)
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Absolving some basic course on finite element methods is required. Last update: KUCERA4 (20.09.2013)
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