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.
Last update: doc. RNDr. Václav Kučera, Ph.D. (21.12.2018)
Cílem této přednášky je seznámit studenty se základy nespojité Galerkinovy metody (DGM), která představuje
moderní vysoce efektivní nástroj pro řešení parciálních diferenciálních rovnic. Bude prezentováno použití DGM pro
případ eliptických, parabolických a hyperbolických rovnic, zejména pak diskrétní formulace a numerická analýza, a
dále budou diskutovány aspekty numerické implementace.
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
Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (07.06.2019)
Ústní zkouška dle sylabu.
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).
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
Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (03.05.2018)
znalosti dle sylabu
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.