@Article{IJNAM-9-2,
author = {},
title = {Superconvergence of Stabilized Low Order Finite Volume Approximation for the Three-Dimensional Stationary Navier-Stokes Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2012},
volume = {9},
number = {2},
pages = {419--431},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2012-IJNAM-639},
url = {https://global-sci.com/article/83480/superconvergence-of-stabilized-low-order-finite-volume-approximation-for-the-three-dimensional-stationary-navier-stokes-equations}
}