A uniform error estimate in time for spectral Galerkin approximations of the magneto‐micropolar fluid equations
Elva E. Ortega-Torres, Marko Antonio Rojas-Medar, Roberto Carlos Cabrales · Numerical Methods for Partial Differential Equations · 2010
Abstract 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