An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators

Abstract : We develop an arbitrary-order primal method for diffusion problems on general polyhedral meshes. The degrees of freedom are scalar-valued polynomials of the same order at mesh elements and faces. The cornerstone of the method is a local (element-wise) discrete gradient reconstruction operator. The design of the method additionally hinges on a least-squares penalty term on faces weakly enforcing the matching between local element- and face-based degrees of freedom. The scheme is proved to optimally converge in the energy norm and in the L2-norm of the potential for smooth solutions. In the lowest-order case, equivalence with the Hybrid Finite Volume method is shown. The theoretical results are confirmed by numerical experiments up to order 4 on several polygonal meshes.
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Computational Methods in Applied Mathematics, Society for Industrial and Applied Mathematics Publications, 2014, 14 (4), pp.461-472. <10.1515/cmam-2014-0018>
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Contributeur : Daniele Antonio Di Pietro <>
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Dernière modification le : lundi 21 mars 2016 - 17:34:42
Document(s) archivé(s) le : jeudi 18 septembre 2014 - 11:30:46

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Daniele Antonio Di Pietro, Alexandre Ern, Simon Lemaire. An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators. Computational Methods in Applied Mathematics, Society for Industrial and Applied Mathematics Publications, 2014, 14 (4), pp.461-472. <10.1515/cmam-2014-0018>. <hal-00978198v2>

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