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A hybridized finite element method for the Stokes problem. (English) Zbl 1361.35128

Summary: A locally conservative hybridized finite element method for Stokes equations is presented and analyzed. The hybridized approach reduces a lot of degrees of freedom, especially for pressure approximation. In our approach the pressure is determined locally up to a constant, therefore, the global stiffness system contains only the average of pressure variable on each cell as unknowns.

MSC:

35Q30 Navier-Stokes equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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[1] Jeon, Y.; Park, E.-J., A hybrid discontinuous Galerkin method for elliptic problems, SIAM J. Numer. Anal., 48, 1968-1983 (2010) · Zbl 1220.65164
[2] Jeon, Y.; Park, E.-J., New locally conservative finite element methods on a rectangular mesh, Numer. Math., 123, 97-119 (2013) · Zbl 1269.65125
[3] Jeon, Y.; Sheen, D., A locking-free locally conservative hybridized scheme for elasticity problems, Japan J. Indust. Appl. Math., 30, 585-603 (2013) · Zbl 1291.74023
[4] Nguyen, N. C.; Peraire, J.; Cockburn, B., A hybridizable discontinuous Galerkin method for Stokes flow, Comput. Methods Appl. Mech. Engrg., 199, 582-597 (2010) · Zbl 1227.76036
[5] Cockburn, B.; Gopalakrishnan, J.; Lazarov, R., Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems, SIAM J. Numer. Anal., 47, 1319-1365 (2009) · Zbl 1205.65312
[6] Wells, G. N., Analysis of an interface stabilised finite element method: the advection-diffusion-reaction equation, SIAM J. Numer. Anal., 49, 87-109 (2011) · Zbl 1226.65097
[7] Hou, T. Y.; Wu, X.-H., A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 134, 169-189 (1997) · Zbl 0880.73065
[8] Brezzi, F.; Fortin, M., Mixed and Hybrid Finite Element Methods (1991), Springer: Springer Berlin, Heidelberg, New York · Zbl 0788.73002
[9] Ern, A.; Guermond, J.-L., Theory and Practice of Finite Elements (2003), Springer
[10] Antonietti, P. F.; Brezzi, F.; Marini, L. D., Stabilizations of the Baumann-Oden DG formulation: the 3D case, Boll. Unione Mat. Ital. (9), 1, 629-643 (2008) · Zbl 1192.65141
[11] Baumann, C. E.; Oden, J. T., A discontinuous \(h p\) finite element method for convection-diffusion problems, Comput. Methods Appl. Mech. Engrg., 175, 311-341 (1999) · Zbl 0924.76051
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