Finite element methods are versatile tools in the computational solution of partial differential equations in physics and engineering. When solutions exhibit localized features, adapted finite element meshes based on error estimations are a frequently used technique to reduce the effort to compute a good approximation. They can accelerate the solution process by orders of magnitude. This short course will deal with the derivation, analysis and application of such methods.
The principal lecturer, Rolf Rannacher, has been among the leading researchers in this field for 15 years and is a driving force behind goal oriented error estimation. This technique produces estimates directly related to measurements relevant in applications. As opposed to many other techniques, it has been applied successfully to a wide class of nonlinear problems. The CBMS conference will give a detailed overview over a posteriori error estimation for a variety of problems in partial differential equations, optimization, and eigenvalue computation. The presentation of theory will be augmented by hands-on sessions allowing participants to explore practical aspects of these techniques.
Although termed "conference", CBMS conferences are actually lecture series with no contributed talks. They are targeted at young researchers who want to learn about the field presented. Nevertheless, we will provide opportunity for short, informal presentations of the participants upon request.
NSF has provided us with funds to defray travel and accomodation costs for a limited number of students. Applications for support should be sent by email to the organizers by March 15th, 2009. Note, however, that CBMS conferences are regional and so support will be preferentially given to participants from Texas and closeby states of the US. In your application for support, please include the name of your PhD advisor, postdoc mentor or a similar reference, if available. We will try to support as many applicants as our budget allows and might therefore ask you to make joint travel arrangements with other participants from your institution.
|Application for support||March 15th, 2009|
|Registration||March 31st, 2009|
|Arrival in College Station||May 17th, 2009|
|Conference||May 18-22, 2009|
The tentative program schedule is as follows:
The lab sessions will be conducted by the organizers and will feature the finite element library deal.II. We will give a basic introduction to the use of this library and show how to construct simple finite element codes. We will also give an overview of the more complicated applications featured in the deal.II tutorial.
We will base lab sessions on version 6.2 of deal.II, which can be downloaded here. We will provide access to computers for everyone during the afternoon lab sessions. However, if you feel more comfortable using your own laptop, you can also download the library to it and follow the installation instructions at this page. Note that deal.II runs right out of the box on Linux and Mac OS X; on Windows, you need the Cygwin environment.