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

Yun-Bo Yang; Qiong-Xiang Kong

Applications of Mathematics (2017)

  • Volume: 62, Issue: 1, page 75-100
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Yang, Yun-Bo, and Kong, Qiong-Xiang. "A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations." Applications of Mathematics 62.1 (2017): 75-100. <http://eudml.org/doc/287557>.

@article{Yang2017,
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.},
author = {Yang, Yun-Bo, Kong, Qiong-Xiang},
journal = {Applications of Mathematics},
keywords = {Navier-Stokes equation; finite element method; variational multiscale; two local Gauss integrations; error correction method},
language = {eng},
number = {1},
pages = {75-100},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations},
url = {http://eudml.org/doc/287557},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Yang, Yun-Bo
AU - Kong, Qiong-Xiang
TI - A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 1
SP - 75
EP - 100
AB - 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.
LA - eng
KW - Navier-Stokes equation; finite element method; variational multiscale; two local Gauss integrations; error correction method
UR - http://eudml.org/doc/287557
ER -

References

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