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Discontinuous Galerkin Methods
Last Updated: 2026-02-05 15:05:34
Abstract
Comprehensive introduction into discontinuous Galerkin methods, which extend the idea of finite element methods and provide an advanced discretization method for a wide range of partial differential equations.The course covers both theoretical, practical and implementational aspects of the methods.
Objective
The goal of the course is to give a comprehensive survey of state of the art theory and practice of discontinuous Galerkin methods. Participants should be enabled to perform theoretical analyses and implement the algorithms.
Content
* DG for first order hyperbolic problems: analysis and implementation * DG for 2nd-order elliptic boundary value problems: analysis and implementation * DG for incompressible flows, * DG for inear elasticity, * DG for Maxwell's equations * A posteriori error estimates for discontinuous Galerkin methods
Resources
Literature
# D.N. Arnold, F. Brezzi, B. Cockburn, L.D. Marini, Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems, SIAM J. Numer. Anal., 39 (2002), 1749-1779. # R. Becker, P. Hansbo, M.G. Larson, Energy norm a posteriori error estimation for discontinuous Galerkin methods, Comput. Methods Appl. Mech. Engrg., 192 (2003), 723-733. # F. Brezzi, L.D. Marini, E. Süli, Discontinuous Galerkin methods for first-order hyperbolic problems, Math. Models Methods Appl. Sci., 14(12) (2004), 1893-1903. # A. Buffa and I. Perugia, Discontinuous Galerkin approximation of the Maxwell eigenproblem, SIAM Numer. Anal., to appear (tech. rep. available at http://www-dimat.unipv.it/~perugia/elpub.html ). # B. Cockburn, G. Kanschat and D. Schötzau, A locally conservative LDG method for the incompressible Navier-Stokes equations, Math. Comp., 74 (2005), 1067-1095. # B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems, SIAM J. Numer. Anal., 35 (1998), 2440-2463. # B. Cockburn and C.-W. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems, J. Sci. Comp., 16 (2001), 173-261. # P. Houston, C. Schwab and E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems, SIAM J. Numer. Anal., 39 (2002), 2133-2163. # P. Houston, D. Schötzau and T. Wihler, Energy norm a posteriori error estimation of hp-adaptive discontinuous Galerkin methods for elliptic problems, Math. Models Meth. Appl. Sci., to appear (available at http://www.math.ubc.ca/~schoetzau/publications.html ). # P. Houston, I. Perugia, A. Schneebeli and D. Schötzau, Interior penalty method for the indefinite time-harmonic Maxwell equations Numer. Math., 100 (2005), 485-518. # P. Houston, I. Perugia and D. Schötzau, Mixed discontinuous Galerkin approximation of the Maxwell operator: Non-stabilized formulation, J. Sci. Comp., 22 (2005), 315-346. # D. Schötzau, C. Schwab and A. Toselli, Mixed hp-DGFEM for incompressible flows, SIAM J. Numer. Anal., 40 (2003), 2171-2194. # T.P. Wihler, Locking-Free DGFEM for Elasticity Problems in Polygons, IMA J. Numer. Anal., 24 (2004), 45-75.
General Information
- Language
- English
- Levels
- MSC
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Discontinuous Galerkin Methods |
|
4 h weekly |