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A sparse grid method for the Navier–Stokes equations based on hyperbolic cross |
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| Authors: | Qingfang Liu Lei Ding Qingchang Liu |
| Institution: | 1. School of Mathematics and Statistics, Xi'an Jiaotong University, , Xi'an 710049, China;2. Center for Computational Geosciences, Xi'an Jiaotong University, , Xi'an 710049, China;3. School of Electronic and Information Engineering, Xi'an Jiaotong University, , Xi'an 710049, China;4. School of Mechanics and Civil & Architecture, Northwestern Polytechnical University, , Xi'an 710129, China |
| Abstract: | 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. |
| Keywords: | sparse grid method Navier– Stokes equations hyperbolic cross stability convergence |