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A finite volume method for the approximation of diffusion operators on distorted meshes. (English) Zbl 0949.65101
This paper deals with diffusion equations on planar domains with arbitrarily irregular grids. The author proposes a finite volume method on the given grid, and it is coupled to another finite volume method on a dual grid. It is shown that the resulting matrix is positive definite, even though it may not be diagonally dominant. Several computational examples are given.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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[1] Ciarlet, P.G., The finite element method for elliptic problems, (1978) · Zbl 0445.73043
[2] Faille, I., A control volume method to solve an elliptic equation on a two-dimensional irregular meshing, Comput. meth. appl. mech. eng., 100, 275, (1992) · Zbl 0761.76068
[3] Ewing, D.J.; Fawkes, A.F.; Griffiths, J.R., Rules governing the numbers of nodes and elements in a finite element mesh, Int. J. num. meth. eng., 2, 597, (1970)
[4] George, P.L.; Borouchaki, H., Triangulation de Delaunay et maillage, (1997)
[5] Morel, J.E.; Dendy, J.E.; Hall, M.L.; White, S.W., A cell centered Lagrangian-mesh diffusion differencing scheme, J. comput. phys., 103, 286, (1992) · Zbl 0763.76052
[6] Hermeline, F., Two coupled particle-finite volume methods using delaunay – voronoi meshes for the approximation of vlasov – poisson and vlasov – maxwell equations, J. comput. phys., 106, (1993) · Zbl 0777.65070
[7] Hermeline, F., Une méthode de volumes finis pour LES équations elliptiques du second ordre, C. R. acad. sci. Paris, 326, 1433, (1998) · Zbl 0912.65104
[8] Kershaw, D.S., Differencing of the diffusion equation in Lagrangian hydrodynamic codes, J. comput. phys., 39, 375, (1981) · Zbl 0467.76080
[9] Lascaux, P.; Theodor, R., Analyse numérique matricielle appliquée à l’art de l’ingénieur, (1986) · Zbl 0601.65016
[10] Letniowski, F.W., Three-dimensional Delaunay triangulations for finite element approximations to a second-order diffusion operator, SIAM J. sci. statist. comput., 13, 765, (1992) · Zbl 0762.65066
[11] Overmars, M.; de Berg, M.; van Kreveld, M.; Schwarzkopf, O., Computational geometry, (1997)
[12] MacNeal, R.H., An asymmetric finite difference network, Q. appl. math., 11, 295, (1953) · Zbl 0053.26304
[13] Shashkov, M.; Steinberg, S., Support-operator finite-difference algorithms for general elliptic problems, J. comput. phys., 118, 131, (1995) · Zbl 0824.65101
[14] C. H. Tong, A comparative study of preconditioned Lanczos methods for non symmetric linear systems, Sandia Report SAND91-8240 UC-404, Jan. 1992, unpublished.
[15] Varga, R.S., Matrix iterative analysis, (1962) · Zbl 0133.08602
[16] Vikhrev, V.V.; Zabaidullin, O.Z., Magnetic field spreading along plasma interface due to the Hall effect, Plasma phys. rep., 20, 867, (1994)
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