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