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Convergence of p-FEM for Maxwell eigenvalue problems

by Z. Chen and R. Hiptmair

(Report number 2004-02)

Abstract
The paper considers the solution of Maxwell eigenvalue problems by the p-version of curl-conforming finite elements on tetrahedral meshes. The asymptotic quasi-optimal convergence of discrete eigenvalues and eigenvectors as p -> \infty is proved. The proof relies on a novel technique combining tools from the calculus of differential forms with techniques for simplicial complexes.

Keywords: Maxwell eigenvalue problem, p-version of edge elements, discrete Poincaré-Friedrichs inequality, Poincaré map

@Techreport{CH04_42,
  author = {Z. Chen and R. Hiptmair},
  title = {Convergence of p-FEM for Maxwell eigenvalue problems},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2004-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2004/2004-02.pdf },
  year = {2004}
}

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