Abstract
We consider stabilized mixed finite element methods for incompressible flow problems which do not require satisfaction of the Babus’ka-Brezzi condition and thus allow for arbitrary velocity-pressure interpolations. Least-squares forms of the Stokes or Navier-Stokes equations are added to the basic Galerkin discretization in order to stabilize the discrete problem without sacrifying accuracy of the solution. Stability and convergence results on non-uniform meshes are given in the whole range from diffusion to convection dominated situations. Numerical results in 2D are presented for low order velocity/pressure interpolation.
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© 1992 Springer Fachmedien Wiesbaden
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Lube, G., Auge, A. (1992). Galerkin/Least-Squares Approximations of Incompressible Flow Problems. In: Vos, J.B., Rizzi, A., Ryhming, I.L. (eds) Proceedings of the Ninth GAMM-Conference on Numerical Methods in Fluid Mechanics. Notes on Numerical Fluid Mechanics (NNFM), vol 35. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-13974-4_28
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DOI: https://doi.org/10.1007/978-3-663-13974-4_28
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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