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Approximation Properties of Vectorial Exponential Functions

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  • 1 CEA, DAM, DIF, 91297 Arpajon, France;
    2 Laboratoire en Informatique Haute Performance Pour le Calcul et la Simulation, CEA, Université Paris-Saclay, 91680 Bruyères-le-Châtel, France;
    3 Laboratoire Jacques-Louis Lions, UMR 7598, Sorbonne Université, 75005 Paris, France;
    4 IMT Atlantique, 29238 Brest, France

Received date: 2022-10-22

  Revised date: 2023-08-14

  Accepted date: 2023-08-16

  Online published: 2024-12-20

Abstract

This contribution is dedicated to the celebration of Rémi Abgrall’s accomplishments in Applied Mathematics and Scientific Computing during the conference “Essentially Hyperbolic Problems: Unconventional Numerics, and Applications”. With respect to classical Finite Elements Methods, Trefftz methods are unconventional methods because of the way the basis functions are generated. Trefftz discontinuous Galerkin (TDG) methods have recently shown potential for numerical approximation of transport equations [6, 26] with vectorial exponential modes. This paper focuses on a proof of the approximation properties of these exponential solutions. We show that vectorial exponential functions can achieve high order convergence. The fundamental part of the proof consists in proving that a certain rectangular matrix has maximal rank.

Cite this article

Christophe Buet, Bruno Despres, Guillaume Morel . Approximation Properties of Vectorial Exponential Functions[J]. Communications on Applied Mathematics and Computation, 2024 , 6(3) : 1801 -1831 . DOI: 10.1007/s42967-023-00310-9

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