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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

CiteScore 2016: 1.09

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

Mathematical Citation Quotient (MCQ) 2016: 0.75

Online
ISSN
1609-9389
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Volume 14, Issue 4 (Oct 2014)

Issues

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

Daniele A. Di Pietro / Alexandre Ern / Simon Lemaire
Published Online: 2014-06-17 | DOI: https://doi.org/10.1515/cmam-2014-0018

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 (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

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Daniele A. Di Pietro and Stella Krell
Journal of Scientific Computing, 2017
[2]
Andrea Cangiani, Zhaonan Dong, and Emmanuil H. Georgoulis
SIAM Journal on Scientific Computing, 2017, Volume 39, Number 4, Page A1251
[4]
Daniele A. Di Pietro and Jérôme Droniou
Mathematical Models and Methods in Applied Sciences, 2017, Volume 27, Number 05, Page 879
[5]
Daniele A. Di Pietro and Ruben Specogna
Journal of Computational Physics, 2016, Volume 326, Page 35
[6]
Bernardo Cockburn, Guosheng Fu, and Weifeng Qiu
IMA Journal of Numerical Analysis, 2016, Page drw029
[7]
Florent Chave, Daniele A. Di Pietro, Fabien Marche, and Franck Pigeonneau
SIAM Journal on Numerical Analysis, 2016, Volume 54, Number 3, Page 1873
[8]
Daniele A. Di Pietro, Jérôme Droniou, and Alexandre Ern
SIAM Journal on Numerical Analysis, 2015, Volume 53, Number 5, Page 2135
[9]
Daniele Boffi, Michele Botti, and Daniele A. Di Pietro
SIAM Journal on Scientific Computing, 2016, Volume 38, Number 3, Page A1508
[10]
Daniele A. Di Pietro and Alexandre Ern
IMA Journal of Numerical Analysis, 2017, Volume 37, Number 1, Page 40
[11]
Christoph Lehrenfeld and Joachim Schöberl
Computer Methods in Applied Mechanics and Engineering, 2016, Volume 307, Page 339
[12]
Jérôme Bonelle, Daniele A. Di Pietro, and Alexandre Ern
Computer Aided Geometric Design, 2015, Volume 35-36, Page 27
[13]
Daniele A. Di Pietro and Alexandre Ern
Comptes Rendus Mathematique, 2015, Volume 353, Number 1, Page 31
[14]
Daniele A. Di Pietro and Alexandre Ern
Computer Methods in Applied Mechanics and Engineering, 2015, Volume 283, Page 1

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