Conditioning of hierarchic p-version Nedelec elements on meshes of curvilinear quadrilaterals and hexahedra

M. Ainsworth, J. Coyle

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

The conditioning of a set of hierarchic basis functions for p-version edge element approximation of the space H(curl) is studied. Theoretical bounds are obtained on the location of the eigenvalues and on the growth of the condition numbers for the mass, curl-curl, and stiffness matrices that naturally arise from Galerkin approximation of Maxwell's equations. The theory is applicable to meshes of curvilinear quadrilaterals or hexahedra in two and three dimensions, respectively, including the case in which the local order of approximation is nonuniform. Throughout, the theory is illustrated with numerical examples that show that the theoretical asymptotic bounds are sharp and are attained within the range of practical computation.
LanguageEnglish
Pages731-750
Number of pages19
JournalSIAM Journal on Numerical Analysis
Volume41
Issue number2
DOIs
Publication statusPublished - 2003

Fingerprint

P-version
Curl
Maxwell equations
Stiffness matrix
Conditioning
Mesh
Edge Elements
H-space
Order of Approximation
Galerkin Approximation
Stiffness Matrix
Condition number
Maxwell's equations
Basis Functions
Three-dimension
Two Dimensions
Eigenvalue
Numerical Examples
Approximation
Range of data

Keywords

  • Eigenvalue bounds
  • finite elements
  • Maxwell equations
  • numerical analysis
  • statistics
  • finite element analysis

Cite this

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abstract = "The conditioning of a set of hierarchic basis functions for p-version edge element approximation of the space H(curl) is studied. Theoretical bounds are obtained on the location of the eigenvalues and on the growth of the condition numbers for the mass, curl-curl, and stiffness matrices that naturally arise from Galerkin approximation of Maxwell's equations. The theory is applicable to meshes of curvilinear quadrilaterals or hexahedra in two and three dimensions, respectively, including the case in which the local order of approximation is nonuniform. Throughout, the theory is illustrated with numerical examples that show that the theoretical asymptotic bounds are sharp and are attained within the range of practical computation.",
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Conditioning of hierarchic p-version Nedelec elements on meshes of curvilinear quadrilaterals and hexahedra. / Ainsworth, M.; Coyle, J.

In: SIAM Journal on Numerical Analysis, Vol. 41, No. 2, 2003, p. 731-750.

Research output: Contribution to journalArticle

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AU - Ainsworth, M.

AU - Coyle, J.

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AB - The conditioning of a set of hierarchic basis functions for p-version edge element approximation of the space H(curl) is studied. Theoretical bounds are obtained on the location of the eigenvalues and on the growth of the condition numbers for the mass, curl-curl, and stiffness matrices that naturally arise from Galerkin approximation of Maxwell's equations. The theory is applicable to meshes of curvilinear quadrilaterals or hexahedra in two and three dimensions, respectively, including the case in which the local order of approximation is nonuniform. Throughout, the theory is illustrated with numerical examples that show that the theoretical asymptotic bounds are sharp and are attained within the range of practical computation.

KW - Eigenvalue bounds

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