Published

Superconvergence of tetrahedral linear finite elements

Long Chen

International Journal of Numerical Analysis and Modeling, 3(3):273-282, 2006.

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Abstract:

  In this paper, we show that the piecewise linear finite element
  solution $u_{h}$ and the linear interpolation $u_{I}$ have
  superclose gradient for tetrahedral meshes, where most elements are
  obtained by dividing approximate parallelepiped into six
  tetrahedra. We then analyze a post-processing gradient recovery
  scheme, showing that the global $L^2$ projection of $\nabla u_h$ is
  a superconvergent gradient approximation to $\nabla u$.