Applications of Mathematics

, Volume 62, Issue 1, pp 75–100 | Cite as

A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations

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Abstract

A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations is presented. Applying the orthogonal projection technique, we introduce two local Gauss integrations as a stabilizing term in the error correction method, and derive a new error correction method. In both the coarse solution computation step and the error computation step, a locally stabilizing term based on two local Gauss integrations is introduced. The stability and convergence of the new error correction algorithm are established. Numerical examples are also presented to verify the theoretical analysis and demonstrate the efficiency of the proposed method.

Keywords

Navier-Stokes equation finite element method variational multiscale two local Gauss integrations error correction method 

MSC 2010

65N15 65N30 65N12 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXi’an Jiao-tong UniversityXi’an, ShaanxiP.R. China
  2. 2.School of Human Settlements and Civil EngineeringXi’an Jiaotong UniversityXi’an, ShaanxiP.R. China

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