Ainsworth, M. and Coyle, J. (2003) *Conditioning of hierarchic p-version Nedelec elements on meshes of curvilinear quadrilaterals and hexahedra.* SIAM Journal on Numerical Analysis, 41 (2). pp. 731-750. ISSN 0036-1429

## 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.

Item type: | Article |
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ID code: | 70 |

Keywords: | Eigenvalue bounds, finite elements, Maxwell equations, numerical analysis, statistics, finite element analysis, Mathematics |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics Faculty of Science > Mathematics and Statistics > Mathematics |

Related URLs: | |

Depositing user: | Mr Derek Boyle |

Date Deposited: | 21 Dec 2005 |

Last modified: | 12 Mar 2012 10:35 |

URI: | http://strathprints.strath.ac.uk/id/eprint/70 |

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