hp-FEM and applications

In this talk, I will present numerical methods for the numerical solution of boundary value problems of partial differential equations by means of finite elements (FEM).
If the solution is (locally) smooth, high order FEM, the so called p-version can accelerate the convergence of the numerical solution to the exact solution.
However, several algorithmic difficulties occur if one uses high order polynomials.
This talk adresses several topics, namely
- domain decomposition preconditioning
- application to optimal control
- applications within PhoenixD.
The presented research results are collaborations with former and current PhD-students and postdocs of my group and the group of Thomas Wick.