Applications of Mathematics, Vol. 62, No. 1, pp. 75-100, 2017
A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations
Yun-Bo Yang, Qiong-Xiang Kong
Received April 17, 2016.
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
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Affiliations: Yun-Bo Yang, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, P. R. China, e-mail: yangyunbo@stu.xjtu.edu.cn; Qiong-Xiang Kong (corresponding author), School of Human Settlements and Civil Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, P. R. China, e-mail: qxkong@mail.xjtu.edu.cn
