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Discrete compactness for p-version of tetrahedral edge elements

by R. Hiptmair

(Report number 2008-31)

Abstract
We consider the first family of H(curl) -conforming Nedéléc finite elements on tetrahedral meshes. Spectral approximation (p-version) is achieved by keeping the mesh fixed and raising the polynomial degree p uniformly in all mesh cells. We prove that the associated subspaces of discretely weakly divergence free piecewise polynomial vector fields enjoy a long conjectured discrete compactness property as $p\to\infty$. This permits us to conclude asymptotic spectral correctness of spectral Galerkin finite element approximations of Maxwell eigenvalue problems.

Keywords:

@Techreport{H08_64,
  author = {R. Hiptmair},
  title = {Discrete compactness for p-version of tetrahedral edge elements},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2008-31},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2008/2008-31.pdf },
  year = {2008}
}

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