Ph.D. Course on

Nodal Discontinuous Galerkin Methods
for solving Partial Differential Equations

Lyngby, August 6rd to 17th 2012

The full course description of the course with learning objectives can be found here [LINK]

The listed topics will be covered in the course and the following book will be used

       J.S. Hesthaven and T. Warburton, 2008, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer Texts in Applied Mathematics 54, Springer Verlag, New York. XIV+500 pages.
Book webpage.

Note: the book will be available in the campus bookshop Polyteknisk Boghandel around the start of the course.

1. Introduction.

Overview of methods for solving partial differential equations and basic introduction to discontinuous Galerkin methods (DG-FEM).

2. DG-FEM in one spatial dimension.

In depth discussion of DG-FEM in 1D for linear problems, numerical fluxes, stability, and basic theoretical results on accuracy.

3. Implementation and numerical aspects

Introduction to appropriate implementations, choices to ensure robust behavior, time-stepping and time-step control, etc.

4. Nonlinear problems

Conservation laws, theoretical aspects for nonlinear problems, filtering and limiting for problems with shocks.

5. Extension to two-dimensions

Extension to simplex based schemes and illustration for general applications.

6. Grid generation

Introduction to basic Matlab based grid generation.

7. Higher-order operators

Extension of DG-FEM to problems with higher spatial derivatives such as Poisson's equation and the incompressible Navier-Stokes equation.

8. Three-dimensional problems and other advanced topics.

Extension to three-dimensional problems. Overview of optional advanced topics such as software packages and GPU accelerated DG-FEM computation.

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Lecturers
Download information

Richard Petersens Plads, DTU - Bygning 321, DK-2800 Lyngby
k.haugland@mat.dtu.dk