Discrete Compactness for p-Version of Tetrahedral Edge Elements

Details Discrete Compactness for p-Version of Tetrahedral Edge Elements Discrete Compactness for p-Version of Tetrahedral Edge Elements

2009-01-07

arxiv.org/abs/0901.0761v1

Mathematics

Numerical Analysis

23 pages

Scientific paper

We consider the first family of $\Hcurl$-conforming Ned\'el\'ec 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.

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