Adaptive variational multiscale methods for incompressible flow based on two local Gauss integrations

Authors:
Haibiao Zheng;Yanren Hou;Feng Shi
Affiliations:
College of Science, Xi'an Jiaotong University, Xi'an 710049, China;College of Science, Xi'an Jiaotong University, Xi'an 710049, China;College of Science, Xi'an Jiaotong University, Xi'an 710049, China
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

We consider variational multiscale (VMS) methods with h-adaptive technique for the stationary incompressible Navier-Stokes equations. The natural combination of VMS with adaptive strategy retains the best features of both methods and overcomes many of their deficits. A reliable a posteriori projection error estimator is derived, which can be computed by two local Gauss integrations at the element level. Finally, some numerical tests are presented to illustrate the method's efficiency.