A posteriori error estimates of finite element method for the time-dependent Oseen equations

Abstract

In this paper, we consider the posteriori error estimates of fully discrete finite element method for the time-dependent Oseen equations. By constructing an appropriate Oseen reconstruction, the optimal error estimates in and norms for velocity and pressure are derived in spatial semidiscrete scheme. Furthermore, a fully discrete scheme is studied based on the backward Euler scheme and the corresponding posteriori error estimators are derived. Finally, some numerical results are presented to verify the performance of the established posteriori error estimators.

Keywords:

• error estimators
• Oseen reconstruction
• backward Euler scheme
• adaptive algorithms

AMS Subject Classifications:

• 65N15
• 65N30
• 76D05

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by CAPES and CNPq of Brazil, the NSF of China (No.11301157), the Doctor Fund of Henan Polytechnic University (B2012-098), the Foundation of Distinguished Young Scientists of Henan Polytechnic University (J2015-05).