Volume 9, Issue 2
Superconvergence of Stabilized Low Order Finite Volume Approximation Forthe Three-dimensional Stationary Navier-Stokes Equations

J. Li, J. Wu, Z. Chen & A. Wang

Int. J. Numer. Anal. Mod., 9 (2012), pp. 419-431

Published online: 2012-09

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  • Abstract
We first analyze a stabilized finite volume method for the three-dimensional stationary Navier-Stokes equations. This method is based on local polynomial pressure projection using low order elements that do not satisfy the inf-sup condition. Then we derive a general superconvergent result for the stabilized finite volume approximation of the stationary Navier-Stokes equations by using a L_2-projection. The method is a postprocessing procedure that constructs a new approximation by using the method of least squares. The superconvergent results have three prominent features. First, they are established for any quasi-uniform mesh. Second, they are derived on the basis of the domain and the solution for the stationary Navier-Stokes problem by solving sparse, symmetric positive definite systems of linear algebraic equations. Third, they are obtained for the finite elements that fail to satisfy the inf-sup condition for incompressible flow. Therefore, this method presented here is of practical importance in scientific computation.
  • Keywords

Navier-Stokes equations stabilized finite volume method local polynomial pressure projection inf-sup condition

  • AMS Subject Headings

35Q10 65N30 76D05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-419, author = {J. Li, J. Wu, Z. Chen and A. Wang}, title = {Superconvergence of Stabilized Low Order Finite Volume Approximation Forthe Three-dimensional Stationary Navier-Stokes Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {2}, pages = {419--431}, abstract = {We first analyze a stabilized finite volume method for the three-dimensional stationary Navier-Stokes equations. This method is based on local polynomial pressure projection using low order elements that do not satisfy the inf-sup condition. Then we derive a general superconvergent result for the stabilized finite volume approximation of the stationary Navier-Stokes equations by using a L_2-projection. The method is a postprocessing procedure that constructs a new approximation by using the method of least squares. The superconvergent results have three prominent features. First, they are established for any quasi-uniform mesh. Second, they are derived on the basis of the domain and the solution for the stationary Navier-Stokes problem by solving sparse, symmetric positive definite systems of linear algebraic equations. Third, they are obtained for the finite elements that fail to satisfy the inf-sup condition for incompressible flow. Therefore, this method presented here is of practical importance in scientific computation.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/639.html} }
TY - JOUR T1 - Superconvergence of Stabilized Low Order Finite Volume Approximation Forthe Three-dimensional Stationary Navier-Stokes Equations AU - J. Li, J. Wu, Z. Chen & A. Wang JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 419 EP - 431 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/639.html KW - Navier-Stokes equations KW - stabilized finite volume method KW - local polynomial pressure projection KW - inf-sup condition AB - We first analyze a stabilized finite volume method for the three-dimensional stationary Navier-Stokes equations. This method is based on local polynomial pressure projection using low order elements that do not satisfy the inf-sup condition. Then we derive a general superconvergent result for the stabilized finite volume approximation of the stationary Navier-Stokes equations by using a L_2-projection. The method is a postprocessing procedure that constructs a new approximation by using the method of least squares. The superconvergent results have three prominent features. First, they are established for any quasi-uniform mesh. Second, they are derived on the basis of the domain and the solution for the stationary Navier-Stokes problem by solving sparse, symmetric positive definite systems of linear algebraic equations. Third, they are obtained for the finite elements that fail to satisfy the inf-sup condition for incompressible flow. Therefore, this method presented here is of practical importance in scientific computation.
J. Li, J. Wu, Z. Chen & A. Wang. (1970). Superconvergence of Stabilized Low Order Finite Volume Approximation Forthe Three-dimensional Stationary Navier-Stokes Equations. International Journal of Numerical Analysis and Modeling. 9 (2). 419-431. doi:
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