The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes
نویسندگان
چکیده
منابع مشابه
The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes
We study the mimetic finite difference discretization of diffusion-type problems on unstructured polyhedral meshes. We demonstrate high accuracy of the approximate solutions for general diffusion tensors, the second-order convergence rate for the scalar unknown and the first order convergence rate for the vector unknown on smooth or slightly distorted meshes, on non-matching meshes, and even on...
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The stability and convergence properties of the mimetic finite difference method for diffusion-type problems on polyhedral meshes are analyzed. The optimal convergence rates for the scalar and vector variables in the mixed formulation of the problem are proved.
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The main goal of this paper is to establish the convergence of mimetic discretizations of the firstorder system that describes linear stationary diffusion on general polyhedral meshes. The main idea of the mimetic finite difference (MFD) method is to mimic the underlying properties of the original continuum differential operators, e.g. conservation laws, solution symmetries, and the fundamental...
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We extend the mimetic finite difference (MFD) method to the numerical treatment of magnetostatic fields problems in mixed div–curl form for the divergence-free magnetic vector potential. To accomplish this task, we introduce three sets of degrees of freedom that are attached to the vertices, the edges, and the faces of the mesh, and two discrete operators mimicking the curl and the gradient ope...
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2006
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2005.05.028