Optimal Error Estimate of the Penalty Finite Element Method for the Micropolar Fluid Equations

Abstract

We present an optimal error estimate of the numerical velocity, pressure, and angular velocity for the fully discrete penalty finite element method of the micropolar equations when the parameters ∊, Δ t, and h are sufficiently small. In order to obtain this estimate, we present the time discretization of the penalty micropolar equation that is based on the backward Euler scheme; the spatial discretization of the time discretized penalty micropolar equation is based on a finite elements space pair (X _h , M _h ) that satisfies some approximations properties.

Keywords:

• Finite elements method
• Fully discrete
• Micropolar fluids
• Penalty

AMS Subject Classification:

• 35Q35
• 76M10
• 76M25
• 65M15

ACKNOWLEDGMENTS

E. O-T. was partially supported by Fondecyt-Chile, grant no. 1040205 and no. 7060025. M. R-M. was partially supported by Fondecyt-Chile, grant no. 7060025.