Functional a posteriori error estimates for parabolic time-periodic boundary value problems

TL;DR

This paper develops guaranteed, fully computable a posteriori error estimates for multiharmonic finite element approximations of parabolic time-periodic boundary value problems, enhancing reliability in practical computations.

Contribution

It introduces functional a posteriori error bounds specifically tailored for multiharmonic finite element methods applied to parabolic time-periodic problems, with proven efficiency.

Findings

Error bounds are guaranteed and fully computable.

Numerical tests confirm the effectiveness of the error estimates.

The approach improves reliability of numerical solutions.

Abstract

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.