Summary
In this paper, a new mixed finite element method for the diffusion equation on polyhedral meshes is proposed. The method is applied to the diffusion equation on meshes with mixed cells when all the coefficients and the source function may have discontinuities inside polyhedral mesh cells. The resulting discrete equations operate only with the degrees of freedom for normal fluxes on the boundaries of cells and one degree of freedom per cell for the solution function.
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References
F. Brezzi and M. Fortin. Mixed and hybrid finite element methods. Springer-Verlag, Berlin 1991
Yu. Kuznetsov. Mixed finite element method in domains of complex geometry. In Abstract Book – 1st International Seminar of SCOMA, number A4/2005 in Reports of the Department of Mathematical Information Technology, Series A, Collections, University of Jyväskylä, Jyväskylä, 2005.
Yu. Kuznetsov. Mixed finite element method for diffusion equations on polygonal meshes with mixed cells. J. Numer. Math., 14(4):305–315, 2006
Yu. Kuznetsov, K. Lipnikov, and M. Shashkov. The mimetic finite difference method on polygonal meshes for diffusion-type equations. Comput. Geosci., 8:301–324, 2004
Yu. Kuznetsov and S. Repin. New mixed finite element method on polygonal and polyhedral meshes. Russian J. Numer. Anal. Math. Modelling, 18(3):261–278, 2003
Yu. Kuznetsov and S. Repin. Convergence analysis and error estimates for mixed finite element method on distorted meshes. J. Numer. Math., 13(1):33–51, 2005
J. E. Roberts and J.-M. Thomas. Mixed and hybrid methods. In P.-G. Ciarlet and J.-L. Lions, editors, Handbook of Numerical Analysis, Vol. II, pages 523–639. North-Holland, Amsterdam, 1991.
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Kuznetsov, Y.A. (2008). Mixed Finite Element Methods on Polyhedral Meshes for Diffusion Equations. In: Glowinski, R., Neittaanmäki, P. (eds) Partial Differential Equations. Computational Methods in Applied Sciences, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8758-5_2
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DOI: https://doi.org/10.1007/978-1-4020-8758-5_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8757-8
Online ISBN: 978-1-4020-8758-5
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