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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

Guarantor:	prof. RNDr. Vít Dolejší, Ph.D., DSc.
Teacher(s):	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

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Annotation -

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.

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

Course completion requirements -

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

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

Literature -

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).

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

Requirements to the exam -

knowledge according to syllabus

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

Syllabus -

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

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

Entry requirements -

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

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