TY - JOUR
T1 - Superconvergence of Stabilized Low Order Finite Volume Approximation for the Three-Dimensional Stationary Navier-Stokes Equations
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, stabilized finite volume method, local polynomial pressure projection, inf-sup condition.
AB - <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>