论文信息 - Error estimates for finite element method solution of the Stokes problem in the primitive variables

Error estimates for finite element method solution of the Stokes problem in the primitive variables

SummaryIn this paper we derive error estimates for a class of finite element approximation of the Stokes equation. These elements, popular among engineers, are conforming lagrangian both in velocity and pressure and therefore based on a mixed variational principle. The error estimates are established from a new Brezzi-type inequality for this kind of mixed formulation. The results are true in 2 or 3 dimensions.

O. Pironneau | M. Bercovier

[1] 川口光年,et al. O. A. Ladyzhenskaya: The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach Sci. Pub. New York-London, 1963, 184頁, 15×23cm, 3,400円. , 1964 .

[2] P. Jamet,et al. Numerical solution of the stationary Navier-Stokes equations by finite element methods , 1973, Computing Methods in Applied Sciences and Engineering.

[3] F. Brezzi. On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[4] Bruce Caswell,et al. The solution of viscous incompressible jet and free-surface flows using finite-element methods , 1974, Journal of Fluid Mechanics.

[5] Robert L. Lee,et al. A comparison of various mixed-interpolation finite elements in the velocity-pressure formulation of the Navier-Stokes equations☆ , 1978 .

[6] P. Raviart. Finite element methods and Navier-Stokes equations , 1979 .