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Proof of uniform convergence for a cell-centered AP discretization of the hyperbolic heat equation on general meshes


Authors: Christophe Buet, Bruno Després, Emmanuel Franck and Thomas Leroy
Journal: Math. Comp. 86 (2017), 1147-1202
MSC (2010): Primary 65M08, 65M12
DOI: https://doi.org/10.1090/mcom/3131
Published electronically: September 12, 2016
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Abstract: We prove the uniform AP convergence on unstructured meshes in 2D of a generalization of the Gosse-Toscani 1D scheme for the hyperbolic heat equation. This scheme is also a nodal extension in 2D of the Jin-Levermore scheme for the 1D case. In 2D, the proof is performed using a new diffusion scheme.


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Christophe Buet
Affiliation: CEA, DAM, DIF, DAM Ile de France, F-91297 Arpajon Cedex, France
Email: christophe.buet@cea.fr

Bruno Després
Affiliation: Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France
Email: despres@ann.jussieu.fr

Emmanuel Franck
Affiliation: Inria Nancy Grand Est and IRMA Strasbourg, 7 rue René Descartes, Strasbourg, France
Email: emmanuel.franck@inria.fr

Thomas Leroy
Affiliation: CEA, DAM, DIF, DAM Ile de France, F-91297 Arpajon Cedex, France
Email: thomas.leroy@cea.fr

DOI: https://doi.org/10.1090/mcom/3131
Received by editor(s): June 26, 2014
Received by editor(s) in revised form: August 8, 2014, July 9, 2015, and November 2, 2015
Published electronically: September 12, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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