Functional a posteriori error estimates for parabolic time-periodic boundary value problems
Provides rigorous error control for a class of parabolic problems relevant to theory and applications, but the method is an extension of existing functional a posteriori techniques.
The paper derives guaranteed and fully computable a posteriori error bounds for multiharmonic finite element approximations of parabolic time-periodic boundary value problems, with numerical tests confirming efficiency.
The paper is concerned with parabolic time-periodic boundary value problems which are of theoretical interest and arise in different practical applications. The multiharmonic finite element method is well adapted to this class of parabolic problems. We study properties of multiharmonic approximations and derive guaranteed and fully computable bounds of approximation errors. For this purpose, we use the functional a posteriori error estimation techniques earlier introduced by S. Repin. Numerical tests confirm the efficiency of the a posteriori error bounds derived.