Numerical Analysis

Course "Numerical Analysis -- Special Topics" (2017-2018)

During this course, we will be acquainted with several classical finite-element techniques with applications in computational fluid dynamics. We will consider standard Galerkin methods, as well as Streamline Upwind Petrov-Galerkin (SUPG) finite-element techniques for convection-diffusion equations. We will also consider techniques, such as by the use of Crouzeix-Raviart, Taylor-Hood elements for (Navier-)Stokes equations. Penalisation methods will be treated for the stabilisation and convenience of solution techniques for Stokes equations. If time permits, an excursion to the pressure-correction method will be made for the treatment of time-dependent Navier-Stokes equations. Divergence free elements might be treated if there is some time left. The participant will do several theoretical take-home assignments, as well as several lab works in matlab.

The following lecture notes are used in the course:

A. Segal. Finite-element methods for the incompressible Navier-Stokes equations. J.M. Burgerscentrum, TU-Delft. (Click here)

These lecture notes are free.

The treatment is not very formal from a mathematical point of view. The most important objective is to acquaint the participant with methodological issues.

The course contains a series of take-home assignments, in which some of them are theoretical, whereas others involve coding in Matlab. (Click here)

Preprogrammed Matlab code can be downloaded here.

Last modified: February 1, 2018.