Published

Optimal anisotropic simplicial meshes for minimizing interpolation errors in $L^p$ norm

Long Chen, Pengtao Sun and Jinchao Xu

Mathematics of Computation, 76(257):179-204, 2007

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Abstract:

  In this paper, we present a new optimal interpolation error estimate
  in $L^p$ norm ($1\leq p\leq \infty$) for finite element simplicial
  meshes in any spatial dimension. A sufficient condition for a mesh
  to be nearly optimal is that it is quasi-uniform under a new metric
  defined by a modified Hessian matrix of the function to be
  interpolated. We also give new functionals for the global moving
  mesh method and obtain optimal monitor functions from the view point
  of minimizing interpolation error in the $L^p$ norm.  Some numerical
  examples are also given to support the theoretical estimates.