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On the stability of bilinear-constant velocity-pressure finite elements. (English) Zbl 0544.76030


MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76M99 Basic methods in fluid mechanics
76E99 Hydrodynamic stability
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References:

[1] Brooks, A.N., Hughes, T.J.R.: Streamline upwind/Petrov Galerkin Formulations for convection dominated flows. Comput. Methods Appl. Mech. Engrg.32, 199-259 (1982) · Zbl 0497.76041 · doi:10.1016/0045-7825(82)90071-8
[2] Sani, R.L., Gresho, P., Lee, R.: On the spurious pressures generated by certain GFEM solutions. Proc. Third Internat. Conf. on Finite Elements in flow problems. Bannff, Canada 1980 · Zbl 0446.76034
[3] Johnson, C., Pitk?ranta, J.: Analysis of some mixed finite element methods related to reduced integration. Technical Report, Chalmers University of Technology, 1980
[4] Gunzburger, M.D., Peterson, J., Nicolaides, R.: On conforming mixed finite element methods for incompressible viscous flow problems. Comput. Math. Appl.8, 67-179 (1982) · Zbl 0483.76038 · doi:10.1016/0898-1221(82)90040-2
[5] Boland, J.M., Nicolaides, R.A.: Stability of finite elements under divergence constraints. SIAM J. Numer. Anal.20, 722-731 (1983) · Zbl 0521.76027 · doi:10.1137/0720048
[6] Girault, V., Raviart, P.-A.: Finite element approximations to the Navier-Stokes equations. Lecture Notes in Mathematics, 749. Berlin, Heidelberg, New York: Springer 1979 · Zbl 0413.65081
[7] Boland, J.M., Nicolaides, R.A.: Stable and semi-stable low order finite elements for viscous flows. SIAM J. Numer. Anal. (to appear) · Zbl 0578.65123
[8] Arnold, D.N., Babu?ka, I., Osborn, J.: Finite Element Methods: Principles for their selection. Laboratory for Numerical Analysis Technical Note BN-997, University of Maryland
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