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Approximation with vectorial exponential functions of solutions of the P N model for the transport of particles

Abstract : Trefftz discontinuous Galerkin (TDG) methods have recently shown potential [6, 27] for numerical approximation of transport equations with exponential modes. This paper focus on a proof of convergence in two-space dimension for the TDG method through the study of the approximation properties of the exponential solutions constructed in [6]. We show that these vectorial exponential functions can achieve high order convergence with a significant gain in term of the number of basis functions compare to more standard discontinuous Galerkin schemes. The fundamental part of the proof is based on discrete Fourier techniques conveniently adapted to the matrices of the problem.
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https://hal.sorbonne-universite.fr/hal-03271588
Contributor : Bruno Després Connect in order to contact the contributor
Submitted on : Saturday, June 26, 2021 - 9:45:33 AM
Last modification on : Thursday, April 7, 2022 - 1:58:32 PM
Long-term archiving on: : Monday, September 27, 2021 - 6:05:43 PM

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  • HAL Id : hal-03271588, version 1

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Christophe Buet, Bruno Despres, Guillaume Morel. Approximation with vectorial exponential functions of solutions of the P N model for the transport of particles. 2021. ⟨hal-03271588⟩

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