hp-FEM for distributed optimal control problems

DI Katharina Hofer

Jan. 8, 2015, 1:45 p.m. S3 057

We consider a distributed optimal control problem which shall be
solved with the hp finite element method. In two dimensions the problem
can be solved with a semismooth Newton-method. There direct solvers
are used, which work in optimal complexity in two dimensions but not
in three. Therefore we are interested in different ways to solve the problem.
We consider a simplified problem which can be written as a saddle
point problem and can be solved - according to Schöberl/Zulehner
- by a special CG-method. Furthermore we tried to extend the results
of Schöberl/Zulehner for piecewise linear and continous elements to highorder
finite elements.