An a posteriori error estimator for the Navier-Stokes equations
Keywords:
error estimate, incompressible fluid, conforming and non-conforming elementsAbstract
This paper presents an a posteriori error for the incompressible Navier-Stokes equations. Two different solutions are computed, one using the Crouzeix-Raviart element and the second one with the non-conforming Fonin-Soulie element. The error estimator is computed as the difference between these solutions. This estimate is used in an adaptative remeshing strategy for steady state solution of the Navier-Stokes equations.
Downloads
References
CRO 73 Crouzeix M. and Raviart P.A., "Conforming and. con-conforming finite
element methods for solving the stationary Stokes equations", RAIRO
, rev. 3, 33-76 (1973)
FOR 83 Fortin M. and Soulie M., "A non-conforming piecewise quadratic finite
element on triangles", Int. J. Numer. Meth. in Engng., Vol. 19,
-520 {1983)
FOR 82 Fortin M., Glowinski R., "Methodes de Lagrangien Augmentes". Dunod,
Paris, 1982.
HET 90 Hetu, J.-F., Pelletier D.H., "Adaptive Remeshing for Incompressible
Viscous Flows". AIAA 21th Fluid Dynamics, Plasma Dynamics. and
Laser Conference, June 18-20, 1990, Seattle.
ODE 86 Oden J.T., Demkowicz 1., Strouboulis T., Devloo P., "Adaptive methods
for problems in solid and fluid mechanics", Accuracy estimates
and adaptive refinements in finite element computations, Edited
by L Babuska, O.C. Zienkiewicz, J. Gago, E.R. de A.Oliveira, John Wiley,
New-York, 1986, 393 p.
PER 87 Peraire J., Vahdati M., Morgan K., Zienkiewicz O.C., "Adaptive Remeshing
for Compressible Flows", J. Comp. Phys, Vol. 72, No 2, 1987.
PIE 93 Pierre. R., Private communications.
ARM 83 Armaly B.F., Durst F., Pereira J.C.F., Schong B.. "Experimental
and Theoretical Investigation of Backward-facing Step Flow". J. Fluid
Mech., Vol127, pp 473-496, 1983.
