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A mixed finite volume scheme for anisotropic diffusion problems on any grid.(English)Zbl 1109.65099

A new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which is easy to implement is presented here [cf.R. A. Klausen andT. F. Russell [Comput. Geosci, 8, No. 4, 341–377 (2004)]. This can apply to any type of grid in any space dimension, with very few conditions on the control volumes. Accurate results are obtained on fairly irregular grids in the case of highly heterogeneous anisotropic problems. Efficiency of the scheme is also shown on several types of grids.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations

Cite

References:

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[2]Aavatsmark I., Barkve T., Boe O., Mannseth T. (1998) Discretization on unstructured grids for inhomogeneous, anisotropic media. Part I: derivation of the methods. J. Sci. Comput. 19, 1700–1716 ·Zbl 0951.65080
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[17]Gallouët T., Herbin R., Vignal M.H. (2000) Error estimate for the approximate finite volume solutions of convection diffusion equations with Dirichlet, Neumann or Fourier boundary conditions. SIAM J. Numer. Anal. 37(6): 1935–1972 ·Zbl 0986.65099 ·doi:10.1137/S0036142999351388
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[19]Klausen R.A., Russell T.F. (2004) Relationships among some locally conservative discretization methods which handle discontinuous coefficients. Comput. Geosci. 8, 341–377 ·Zbl 1124.76030 ·doi:10.1007/s10596-005-1815-9
[20]Kuznetsov Y., Repin S. (2005) Convergence analysis and error estimates for mixed finite element method on distorted meshes. J. Numer. Math. 13(1): 33–51 ·Zbl 1069.65114 ·doi:10.1515/1569395054068973
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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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