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Adaptive variational multiscale method for the Stokes equations
Author(s) -
Song Lina,
Hou Yanren,
Zheng Haibiao
Publication year - 2012
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3716
Subject(s) - a priori and a posteriori , estimator , polygon mesh , mathematical optimization , residual , scale (ratio) , mathematics , computer science , adaptive mesh refinement , series (stratigraphy) , construct (python library) , algorithm , computational science , geometry , paleontology , philosophy , statistics , physics , epistemology , quantum mechanics , biology , programming language
SUMMARY An adaptive variational multiscale method for the Stokes equations is presented in this paper. We solve the coarse scale problem on the coarse mesh and approximate the fine scale solution by solving a series of local residual equations defined on some local fine grids, which can be implemented in parallel. In addition, we also propose a reliable local a posteriori error estimator and construct an adaptive algorithm based on the corresponding a posterior error estimate. Finally, numerical examples are presented to verify the algorithm.Copyright © 2012 John Wiley & Sons, Ltd.