Superconvergence of Stabilized Low Order Finite Volume Approximation for the Three-Dimensional Stationary Navier-Stokes Equations
Year: 2012
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-639
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 2 : pp. 419–431
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Navier-Stokes equations stabilized finite volume method local polynomial pressure projection inf-sup condition.