hp-FEM for distributed optimal control problems

DI Katharina Hofer

Jan. 8, 2015, 12:45 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.