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A sparse grid method for the Navier–Stokes equations based on hyperbolic cross
Author(s) -
Liu Qingfang,
Ding Lei,
Liu Qingchang
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2845
Subject(s) - sparse grid , discretization , mathematics , grid , convergence (economics) , truncation (statistics) , stability (learning theory) , series (stratigraphy) , navier–stokes equations , mathematical analysis , geometry , computer science , compressibility , paleontology , statistics , biology , economic growth , aerospace engineering , engineering , machine learning , economics
A sparse grid method for the time‐dependent Navier–Stokes equations based on hyperbolic cross approximation is considered in this article. Subsequent truncation of the associated series expansion results in a sparse grid discretization. Stability and convergence of the fully discrete sparse grid method are established. Finally, the numerical experiment is presented to show the effectiveness of this sparse grid method. Copyright © 2013 John Wiley & Sons, Ltd.