A family of 3D continuously differentiable finite elements on tetrahedral grids

  • Authors:

  • Shangyou Zhang

  • Affiliations:

  • Department of Mathematical Sciences, University of Delaware, DE 19716, USA

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2009

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Abstract

A family of continuously differentiable piecewise polynomials of degree 9 and higher, on general tetrahedral grids, is constructed, by simplifying and extending the P"9 element of Zenisek. A mathematical justification and numerical tests are presented. The current computing power is still limited for the computation with 3D C"1 finite elements in general. The construction here mainly serves the purposes of understanding and ensuring the approximation properties of C"1 finite elements spaces on tetrahedral grids. In particular, this construction indicates that the 3D divergence-free C"0-P"k elements have the full order of approximation for any degree k=8.