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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Uniform-in-time error estimates for spectral Galerkin approximations of a mass diffusion model


Authors: J. V. Gutiérrez-Santacreu and M. A. Rojas-Medar
Journal: Math. Comp. 81 (2012), 191-218
MSC (2010): Primary 35Q35, 65M12, 65M15, 76D05
Published electronically: June 28, 2011
MathSciNet review: 2833492
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Abstract: The goal of this paper is to present uniform-in-time error estimates by considering spectral Galerkin approximations of the Kazhikhov-Smagulov model for strong solutions. To be more precise, we derive an optimal uniform-in-time error bound in the $ \boldsymbol{H}^1\times H^2$ norm for the velocity and density approximations being stated in Theorem 6.


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Additional Information

J. V. Gutiérrez-Santacreu
Affiliation: Departmento Matemática Aplicada I, Universidad de Sevilla, E. T. S. I. Informática. Avda. Reina Mercedes, s/n. 41012 Sevilla, Spain
Email: juanvi@us.es

M. A. Rojas-Medar
Affiliation: Grupo de Matemática Aplicada, Dpto. de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Casilla 447, Chillán, Chile
Email: marko@ueubiobio.cl.

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02491-9
PII: S 0025-5718(2011)02491-9
Keywords: Fluids with diffusion, spectral Galerkin method, error estimates.
Received by editor(s): August 31, 2009
Received by editor(s) in revised form: October 9, 2010
Published electronically: June 28, 2011
Additional Notes: The first author’s work was partially supported by project MTM2006-07932, Spain.
The second author’s work was partially supported by project MTM2006-07932, Spain and Grant 1080628, Fondecyt-Chile.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.