Pointwise Error Estimate for Spectral Galerkin Approximations of Micropolar Equations

The goal of this article is to present pointwise time error estimates in suitable Hilbert spaces by considering spectral Galerkin approximations of the micropolar fluid model for strong solutions. In fact, we use the properties of the Stokes and Lamé operators for prove the pointwise convergence rate in the H²-norm for the ordinary velocity and microrotational velocity and the pointwise convergence rate in the L²-norm for the time-derivative of both velocities. The novelty of our method is that we do not impose any compatibility conditions in the initial data.