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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A Trefftz method with reconstruction of the normal derivative applied to elliptic equations
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by Bruno Després, Maria El Ghaoui and Toni Sayah HTML | PDF
Math. Comp. 91 (2022), 2645-2679 Request permission

Abstract:

This article deals with the application of the Trefftz method to the Laplace problem. We introduce a new discrete variational formulation using a penalisation of the continuity of the solution on the edges which is compatible with the discontinuity of the Trefftz basis functions in the cells. We prove the existence and uniqueness of the discrete solution. A high order error estimate is established. The theory is validated with several numerical experiments for different values of the mesh size, the order of the method and the penalisation coefficient. It is found that the penalisation coefficient has an influence on the conditioning of the method.
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Additional Information
  • Bruno Després
  • Affiliation: Laboratoire Jacques-Louis Lions, Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, F-75005 Paris, France
  • Email: bruno.despres@sorbonne-universite.fr
  • Maria El Ghaoui
  • Affiliation: Laboratoire Jacques-Louis Lions, Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, F-75005 Paris, France; and Laboratoire de Mathétiques et Applications, Unité de recherche Mathématiques et Modélisation, Faculté des Sciences, Université Saint-Joseph, B.P 11-514 Riad El Solh, Beyrouth 1107 2050, Liban
  • ORCID: 0000-0002-7545-2314
  • Email: maria.ghaoui@net.usj.edu.lb
  • Toni Sayah
  • Affiliation: Laboratoire de Mathétiques et Applications, Unité de recherche Mathématiques et Modélisation, Faculté des Sciences, Université Saint-Joseph, B.P 11-514 Riad El Solh, Beyrouth 1107 2050, Liban
  • MR Author ID: 704612
  • Email: toni.sayah@usj.edu.lb
  • Received by editor(s): October 23, 2020
  • Received by editor(s) in revised form: November 23, 2021, March 12, 2022, and April 25, 2022
  • Published electronically: July 15, 2022
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 2645-2679
  • MSC (2020): Primary 35A25
  • DOI: https://doi.org/10.1090/mcom/3756
  • MathSciNet review: 4473099