Numerical Algorithms

, Volume 78, Issue 2, pp 569–597 | Cite as

An explicitly uncoupled VMS stabilization finite element method for the time-dependent Darcy-Brinkman equations in double-diffusive convection

Original Paper
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Abstract

In this article, a full explicitly uncoupled variational multiscale (VMS) stabilization finite element method for solving the Darcy-Brinkman equations in double-diffusive convection is proposed. This method introduces three uncoupled VMS treatments for the velocity, the temperature, and the concentration as the postprocessing steps at each time step, respectively. We only need first to solve three full decoupled linear problems and then to solve three full decoupled postprocessing problems. This method is easy to implement because the existing codes can be used. The unconditional stability is proved and the a priori error estimates are derived. A series of numerical experiments are also given to confirm the theoretical analysis and to demonstrate the efficiency of the new method.

Keywords

Double-diffusive convection Darcy-Brinkman Finite element method Variational multiscale method Uncoupled and modular postprocessing 

Mathematics Subject Classification (2010)

65N15 65N30 65N12 65M12 

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Notes

Acknowledgements

This work was supported by the Natural Science Foundation of China (NSFC) under grants 11371287 and 61663043 and the Natural Science Basic Research Plan in Shaanxi Province of China under grant 2016JM5077.

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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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