Topics in Scientific Computing, procse13

The course's topic 2013 is

Discontinuous Galerkin finite element method for conservation laws

This course is given as a one-week compact course and a final project.

Intended Audience

Everybody who is interested in numerically solving partial differential equations

Schedule

March 11-15, 2012, full days, 4 hours of lectures in the mornings, 4 hours of hands-on exercises/computer lab during afternoons

Place

NA Department (Teknikringen 14), room 319

Teacher

Dr. Vadym Aizinger, University of Erlangen-Nuremberg, Department of Mathematics

Course Contents

The topic of this course is an introduction of discontinuous Galerkin (DG) finite element method for solving hyperbolic and parabolic partial differential equations (PDE) and systems of PDEs. Ever increasing popularity of the DG schemes in the computational fluid dynamics and other fields of computational science and engineering is due to a number of unique advantages offered by this type of numerical method which combines the high order approximation capabilities of the traditional finite elements with the local conservation properties and the robustness of the finite volumes. On top of that, the DG method supports different types of mesh and approximation space adaptivity; the implementations based on it demonstrate outstanding performance on parallel computing clusters.

The objective of this course is to present the students the basic theoretical tools and practical implementation details of the method. The topics include

Conservation laws for a continuum medium.
The concept of discontinuous finite elements.
Discontinuous shape functions in one, two, and three dimensions.
Pure convection problems.
Convection-diffusion problems.
Non-linear problems.
Compressible fluid flows.

The course work includes programming assignments that require an implementation of 1D and 2D discontinuous Galerkin finite element solvers for convection-diffusion problems.

Examination

A homework project

Further information about the course is given by

Michael Hanke, hanke@nada.kth.se, (course administrator).