Technical Note: A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes

Mark Ainsworth; Richard Rankin

doi:10.1002/num.20663

Technical Note: A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes

Mark Ainsworth, Richard Rankin

Research output: Journal Publication › Article › peer-review

18 Citations (Scopus)

Abstract

We obtain a computable lower bound on the value of the interior penalty parameters sufficient for the existence of a unique discontinuous Galerkin finite element approximation of a second order elliptic problem. The bound obtained is valid for meshes containing an arbitrary number of hanging nodes and elements of arbitrary nonuniform polynomial order.

Original language	English
Pages (from-to)	1099-1104
Number of pages	6
Journal	Numerical Methods for Partial Differential Equations
Volume	28
Issue number	3
DOIs	https://doi.org/10.1002/num.20663
Publication status	Published - May 2012
Externally published	Yes

Keywords

discontinuous Galerkin method
finite element
interior penalty method

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1002/num.20663

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title = "Technical Note: A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes",

abstract = "We obtain a computable lower bound on the value of the interior penalty parameters sufficient for the existence of a unique discontinuous Galerkin finite element approximation of a second order elliptic problem. The bound obtained is valid for meshes containing an arbitrary number of hanging nodes and elements of arbitrary nonuniform polynomial order.",

keywords = "discontinuous Galerkin method, finite element, interior penalty method",

author = "Mark Ainsworth and Richard Rankin",

year = "2012",

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doi = "10.1002/num.20663",

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T2 - A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes

AU - Ainsworth, Mark

AU - Rankin, Richard

PY - 2012/5

Y1 - 2012/5

N2 - We obtain a computable lower bound on the value of the interior penalty parameters sufficient for the existence of a unique discontinuous Galerkin finite element approximation of a second order elliptic problem. The bound obtained is valid for meshes containing an arbitrary number of hanging nodes and elements of arbitrary nonuniform polynomial order.

AB - We obtain a computable lower bound on the value of the interior penalty parameters sufficient for the existence of a unique discontinuous Galerkin finite element approximation of a second order elliptic problem. The bound obtained is valid for meshes containing an arbitrary number of hanging nodes and elements of arbitrary nonuniform polynomial order.

KW - discontinuous Galerkin method

KW - finite element

KW - interior penalty method

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U2 - 10.1002/num.20663

DO - 10.1002/num.20663

M3 - Article

AN - SCOPUS:84858072004

SN - 0749-159X

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JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 3

ER -

Technical Note: A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes

Abstract

Keywords

ASJC Scopus subject areas

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