Functional a posteriori error estimates for parabolic time-periodic problems

Dipl.-Ing.in Monika Wolfmayr

Nov. 6, 2014, 1 p.m. S2 416-2

The multiharmonic finite element method is very suitable for solving parabolic time-periodic boundary value problems and parabolic time-periodic optimal control problems where the former one appears as PDE constraints. In this talk, we present new functional a posteriori estimates that can be used to derive guaranteed and fully computable error bounds and to construct fully adaptive versions of the multiharmonic FEM in space and time. The functional a posteriori error estimation techniques are based on the works by S. Repin, but the multiharmonic finite element analysis contains proper changes regarding the special features of the approximation via truncated Fourier series and the used variational framework. We discuss implementation issues and present first numerical results including the computation of error bounds corresponding to single Fourier modes as well as of the overall error bounds.