Sparsity optimized high order finite element functions for H(div) on simplices

@article{Beuchler2012SparsityOH,
  title={Sparsity optimized high order finite element functions for H(div) on simplices},
  author={Sven Beuchler and Veronika Pillwein and Sabine Zaglmayr},
  journal={Numerische Mathematik},
  year={2012},
  volume={122},
  pages={197-225}
}
This paper deals with conforming high-order finite element discretizations of the vectorvalued function space H(div) in 2 and 3 dimensions. A new set of hierarchic basis functions on simplices with the following two main properties is introduced. When working with an affine, simplicial triangulation, first, the divergence of the basis functions is L2-orthogonal, and secondly, the L2-inner product of the interior basis functions is sparse with respect to the polynomial degree p. The construction… CONTINUE READING
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High Order Finite Elements for Electromagnetic Field Computation

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