Compact high order complete flux schemes

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Abstract

In this paper we outline the complete flux scheme for an advection-diffusion-reaction model problem. The scheme is based on the integral representation of the flux, which we derive from a local boundary value problem for the entire equation, including the source term. Consequently, the flux consists of a homogeneous part, corresponding to the advection-diffusion operator, and an inhomogeneous part, taking into account the effect of the source term. We apply (weighted) Gauss quadrature rules to derive the standard complete flux scheme, as well as a compact high order variant. We demonstrate the performance of both schemes.

Original languageEnglish
Title of host publicationSpectral and high order methods for partial differential equations ICOSAHOM 2016
Subtitle of host publicationSelected Papers from the ICOSAHOM conference, June 27-July 1, 2016, Rio de Janeiro, Brazil
EditorsM.L. Bittencourt, N. Dumont, J.S. Hesthaven
Place of PublicationCham
PublisherSpringer
Pages561-570
Number of pages10
ISBN (Print)978-3-319-65870-4
DOIs
Publication statusPublished - 2017
Event11th International Conference on Spectral and High-Order Methods (ICOSAHOM 2016) - Rio Othon Palace Copacabana, Rio de Janeiro, Brazil
Duration: 27 Jun 20161 Jul 2016
Conference number: 11

Publication series

NameLecture Notes in Computational Science and Engineering
Volume119
ISSN (Print)1439-7358

Conference

Conference11th International Conference on Spectral and High-Order Methods (ICOSAHOM 2016)
Abbreviated titleICOSAHOM2016
CountryBrazil
CityRio de Janeiro
Period27/06/161/07/16

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    ten Thije Boonkkamp, J. H. M., & Anthonissen, M. J. H. (2017). Compact high order complete flux schemes. In M. L. Bittencourt, N. Dumont, & J. S. Hesthaven (Eds.), Spectral and high order methods for partial differential equations ICOSAHOM 2016: Selected Papers from the ICOSAHOM conference, June 27-July 1, 2016, Rio de Janeiro, Brazil (pp. 561-570). (Lecture Notes in Computational Science and Engineering; Vol. 119). Cham: Springer. https://doi.org/10.1007/978-3-319-65870-4_40