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Course, academic year 2019/2020
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Numerical Solution of Evolutionary Equations - NMNV536
Title in English: Numerické řešení evolučních rovnic
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. RNDr. Václav Kučera, Ph.D.
Class: M Mgr. NVM
M Mgr. NVM > Povinně volitelné
Classification: Mathematics > Numerical Analysis
Incompatibility : NNUM112
Interchangeability : NNUM112
Annotation -
Last update: T_KNM (11.05.2015)
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.
Course completion requirements -
Last update: doc. RNDr. Václav Kučera, Ph.D. (10.06.2019)

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.

Literature - Czech
Last update: KUCERA4 (28.04.2015)

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

Requirements to the exam -
Last update: doc. RNDr. Václav Kučera, Ph.D. (28.02.2018)

The exam is in oral form. The requirements are given by the scope covered in the lecture.

Syllabus -
Last update: KUCERA4 (20.09.2013)

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.

Entry requirements -
Last update: KUCERA4 (20.09.2013)

Absolving some basic course on finite element methods is required.

 
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