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Fundamentals of Discontinuous Galerkin Method - NMNV540

Title:	Základy nespojité Galerkinovy metody
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	yes / unlimited
Key competences:	4EU+ Flagship 3
State of the course:	taught
Language:	English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Vít Dolejší, Ph.D., DSc.
Class:	M Mgr. NVM M Mgr. NVM > Povinně volitelné
Classification:	Mathematics > Numerical Analysis
Incompatibility :	NNUM069
Interchangeability :	NNUM069
Is interchangeable with:	NNUM069

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (12.09.2013)

The goal of this lecture is to present the base of the discontinuous Galerkin method (DGM) which exhibits an efficient tool for the solution of partial differential equations. We present a use of DGM for elliptic, parabolic and hyperbolic equations, namely the discretization, numerical analysis and some aspects of a numerical implementation.

Course completion requirements -

Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (29.04.2020)

Oral examination according to the sylabus

Solving and sending by email 3 tests ( http://msekce.karlin.mff.cuni.cz/~dolejsi/Vyuka/DGM.html ),

possible discussion using zoom

Literature -

Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (30.11.2021)

Lecture notes at https://www2.karlin.mff.cuni.cz/~dolejsi/Vyuka/LectureNotes_DGM.pdf

V. Dolejsi, M. Feistauer: Discontinuous Galerkin Method - Analysis and Applications to Compressible Flow, Springer-Verlag, 2015.

Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, L.Donatella: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, No.5, 1749-1779 (2002).

Cockburn, Bernardo: An introduction to the discontinuous Galerkin method for convection-dominated problems. Quarteroni, Alfio (ed.) et al., Advanced numerical approximation of nonlinear hyperbolic equations. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 23--28, 1997. Berlin: Springer. Lect. Notes Math. 1697, 151-268 (1998).

Requirements to the exam -

Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (03.05.2018)

knowledge according to syllabus

Syllabus -

Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (13.02.2022)

Discontinuous Galerkin method (DGM).

Solution of elliptic, parabolic and hyperbolic problems by DGM.

A priori error estimates.

Numerical implementation

https://www2.karlin.mff.cuni.cz/~dolejsi/Vyuka/DGM.html

Entry requirements -

Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (03.05.2018)

basic knwledge of finite element methods and weak solution of partial differential equations