Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods

Jan Nordström; Andrew R. Winters

doi:10.1007/s10915-021-01434-x

Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods

Jan Nordström, Andrew R. Winters

Mathematics and Applied Mathematics

Linköping University

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits that the DG approximation is constructed from polynomial basis functions and that integrals are approximated with high-order accurate Legendre–Gauss–Lobatto quadrature. The theoretical discussion re-contextualizes stable filtering results for finite difference methods into the DG setting. Numerical tests verify and validate the underlying theoretical results.

Original language	English
Article number	17
Journal	Journal of Scientific Computing
Volume	87
Issue number	1
DOIs	https://doi.org/10.1007/s10915-021-01434-x
Publication status	Published - Apr 2021

Keywords

Discontinuous Galerkin
Filtering
Stability
Transmission problem

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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10.1007/s10915-021-01434-x

Cite this

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abstract = "We prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits that the DG approximation is constructed from polynomial basis functions and that integrals are approximated with high-order accurate Legendre–Gauss–Lobatto quadrature. The theoretical discussion re-contextualizes stable filtering results for finite difference methods into the DG setting. Numerical tests verify and validate the underlying theoretical results.",

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AB - We prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits that the DG approximation is constructed from polynomial basis functions and that integrals are approximated with high-order accurate Legendre–Gauss–Lobatto quadrature. The theoretical discussion re-contextualizes stable filtering results for finite difference methods into the DG setting. Numerical tests verify and validate the underlying theoretical results.

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KW - Stability

KW - Transmission problem

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Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods

Abstract

Keywords

ASJC Scopus subject areas

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