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A uniform error estimate in time for spectral Galerkin approximations of the magneto‐micropolar fluid equations
Author(s) -
OrtegaTorres E.E.,
RojasMedar M.A.,
Cabrales R.C.
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20651
Subject(s) - mathematics , galerkin method , bounded function , mathematical analysis , compressibility , boundary value problem , domain (mathematical analysis) , exponential function , finite element method , physics , mechanics , thermodynamics
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 H 1 and L 2 ‐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