Summary
We give a brief overview of our recent work on the edge stabilization method for flow problems. The application examples are convection-diffusion, with small diffusion parameter, and a generalized Stokes model.
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Brezzi, F, Fortin, M. (1991): Mixed and Hybrid Finite Element Methods. Springer, New York
Brezzi, F., Hughes, T.J.R., Marini, L.D., Russo, A., Suli, E.A. (1999): A priori error analysis of residual-free bubbles for advection-diffusion problems. SIAM J. Numer. Anal., 36, 1933–1948
Burman, E., Hansbo, P. (2002): Edge stabilization for Galerkin approximations of convection-diffusion problems. Chalmers Finite Element Center Preprint 2002-17
Burman, E., Hansbo, P. (2003): Edge stabilization for the generalized Stokes problem: a continuous interior penalty method. Chalmers Finite Element Center Preprint 2003-16
Codina, R., Blasco, J. (2000): Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations. Numer. Math., 87, 59–81
Douglas, J., Dupont, T. (1976): Interior penalty procedures for elliptic and parabolic Galerkin methods, in: R. Glowinski, R., Lions, J. L. (eds) Computing Methods in Applied Sciences. Springer Berlin
Guermond, J.L. (1999): Stabilization of Galerkin approximations of transport equations by subgrid modeling. M2AN Math. Model. Numer. Anal., 33, 1293–1316
Johnson, C., Nävert, U., Pitkáranta, J. (1984): Finite element methods for linear hyperbolic equations. Comput. Methods Appl. Mech. Engrg., 45, 285–312
Johnson, C., Pitkäranta, J. (1986): An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation, Math. Comp., 46, 427–444.
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© 2004 Springer-Verlag Berlin Heidelberg
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Burman, E., Hansbo, P. (2004). The Edge Stabilization Method for Finite Elements in CFD. In: Feistauer, M., DolejÅ¡Ã, V., Knobloch, P., Najzar, K. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18775-9_17
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DOI: https://doi.org/10.1007/978-3-642-18775-9_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62288-5
Online ISBN: 978-3-642-18775-9
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