Finite Volume Method for Nonlinear Transmission Problems

B. Andreianov, F. Boyer, and F. Hubert. Discrete duality finite volume schemes for Leray-Lions type elliptic problems on general 2D-meshes. Numer. Methods Partial Differential Equations, 23(1):145–195, 2007.
Article MATH MathSciNet Google Scholar
F. Boyer and F. Hubert. Finite volume method for 2d linear and nonlinear elliptic problems with discontinuities. Technical report, Université de Provence, Marseille, France, 2006. http://hal.archives-ouvertes.fr/hal-00110436.
Y. Coudière, J.-P. Vila, and P. Villedieu. Convergence rate of a finite volume scheme for a two-dimensional convection-diffusion problem. M2AN Math. Model. Numer. Anal., 33(3):493–516, 1999.
Article MATH MathSciNet Google Scholar
K. Domelevo and P. Omnes. A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids. M2AN Math. Model. Numer. Anal., 39(6):1203–1249, 2005.
Article MATH MathSciNet Google Scholar
M. Feistauer and V. Sobotíková. Finite element approximation of nonlinear elliptic problems with discontinuous coefficients. RAIRO Modél. Math. Anal. Numér., 24(4):457–500, 1990.
MATH Google Scholar
R. Glowinski. Numerical Methods for Nonlinear Variational Problems. Springer Series in Computational Physics. Springer-Verlag, New York, 1984.
MATH Google Scholar
F. Hermeline. Approximation of diffusion operators with discontinuous tensor coefficients on distorted meshes. Comput. Methods Appl. Mech. Engrg., 192(16-18):1939–1959, 2003.
Article MATH MathSciNet Google Scholar
W. B. Liu. Degenerate quasilinear elliptic equations arising from bimaterial problems in elastic-plastic mechanics. Nonlinear Anal., 35(4):517–529, 1999.
Article MathSciNet Google Scholar
W. B. Liu. Finite element approximation of a nonlinear elliptic equation arising from bimaterial problems in elastic-plastic mechanics. Numer. Math., 86(3):491–506, 2000.
Article MATH MathSciNet Google Scholar

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Centre de Mathématiques et Informatique, Université de Provence, 39, rue F. Joliot Curie, 13453, Marseille Cedex 13, France
Franck Boyer & Florence Hubert

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Franck Boyer
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Florence Hubert
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Institute of Computational Mathematics, Johannes Kepler University Linz, Altenbergerstr. 69, 4040, Linz, Austria
Ulrich Langer & Walter Zulehner &
Institute of Analysis and Scientific Computing — CMCS, Ecole Polytechnique Fédérale de Lausanne EPFL SB IACS CMCS Bâtiment MA, Station 8, 1015, Lausanne, Switzerland
Marco Discacciati
Department of Applied Physics and Applied Mathematics, Columbia University, 500 W. 120th Street, MC 4701, 10027, New York, NY, USA
David E. Keyes
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185, USA
Olof B. Widlund

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Boyer, F., Hubert, F. (2008). Finite Volume Method for Nonlinear Transmission Problems. In: Langer, U., Discacciati, M., Keyes, D.E., Widlund, O.B., Zulehner, W. (eds) Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75199-1_56

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DOI: https://doi.org/10.1007/978-3-540-75199-1_56
Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-540-75199-1
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