Multiharmonic Finite Element Analysis of Parabolic Time-Periodic Simulation and Optimal Control Problems
Dipl.-Ing.in Monika WolfmayrApril 3, 2014, 11 a.m. K 224B
In this talk, we consider the construction and analysis of efficient and robust numerical methods for linear parabolic time-periodic simulation and optimal control problems. The mathematical and numerical analysis include existence and uniqueness results in a new variational framework and full a priori and a posteriori error estimates in space and time. The discretization of the parabolic time-periodic problems is based on the multiharmonic finite element method, which is a very natural approach to discretize this type of parabolic problems. Moreover, we present new algebraic multilevel preconditioned minimal residual methods for solving the discrete problems, which have saddle point structure. These methods are robust and of optimal complexity, which is impressively confirmed by theoretical as well as numerical results.