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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year

IMPACT FACTOR 2016: 1.097

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SCImago Journal Rank (SJR) 2016: 0.872
Source Normalized Impact per Paper (SNIP) 2016: 0.887

Mathematical Citation Quotient (MCQ) 2016: 0.75

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Volume 14, Issue 4 (Oct 2014)


An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators

Daniele A. Di Pietro
  • University Montpellier 2, I3M, 34057 Montpellier Cedex 5, France
  • Email:
/ Alexandre Ern
  • University Paris-Est, CERMICS (ENPC), 6–8 avenue Blaise Pascal, 77455 Marne-la-Vallée Cedex 2, France
  • Email:
/ Simon Lemaire
  • University Paris-Est, CERMICS (ENPC), 6–8 avenue Blaise Pascal, 77455 Marne-la-Vallée Cedex 2, France
  • Email:
Published Online: 2014-06-17 | DOI: https://doi.org/10.1515/cmam-2014-0018


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 (elementwise) 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.

Keywords: Diffusion; General Meshes; Arbitrary-Order; Gradient Reconstruction

MSC: 65N30; 65N08; 76R50

About the article

Received: 2014-04-13

Revised: 2014-05-29

Accepted: 2014-06-02

Published Online: 2014-06-17

Published in Print: 2014-10-01

Citation Information: Computational Methods in Applied Mathematics, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2014-0018.

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© 2014 by De Gruyter. Copyright Clearance Center

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