A uniform error estimate in time for spectral Galerkin approximations of the magneto‐micropolar fluid equations

We consider Galerkin approximations for the equations modeling the motion of an incompressible magneto‐micropolar fluid in a bounded domain. We derive an optimal uniform in time error bound in the H¹ and L² ‐norms for the velocity. This is done without explicit assumption of exponential stability for a class of solutions corresponding to decaying external force fields. Our study is done for no‐slip boundary conditions, but the results obtained are easily extended to the case of periodic boundary conditions. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 689–706, 2012