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Computation of Maxwell eigenvalues on curvilinear domains using hp-version Nédélec elements

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • M. Ainsworth

    (University of Strathclyde, Department of Mathematics)

  • J. Coyle

    (University of Strathclyde, Department of Mathematics)

Abstract

Summary In this paper we present and numerically verify theoretical bounds on the growth of the conditioning number for an H(curl)-conforming basis suitable for variable order approximation on curvilinear quadrilateral or hexahedral meshes. These bounds are given explicitly in terms of the maximum polynomial degree of approximation employed throughout the mesh. Additionally, numerical examples demonstrating the use of the basis in the context of electromagnetic eigenvalue problems on curved domains with reentrant comers are given. These examples also serve as a preliminary investigation of hp-refinement in computing eigenvalues corresponding to both singular and non-singular eigenfunctions on curvilinear domains.

Suggested Citation

  • M. Ainsworth & J. Coyle, 2003. "Computation of Maxwell eigenvalues on curvilinear domains using hp-version Nédélec elements," Springer Books, in: Franco Brezzi & Annalisa Buffa & Stefania Corsaro & Almerico Murli (ed.), Numerical Mathematics and Advanced Applications, pages 219-231, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2089-4_20
    DOI: 10.1007/978-88-470-2089-4_20
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