Piecewise Linear Orthogonal Approximation

  • Authors:
  • Andreas App;Ulrich Reif

  • Affiliations:
  • appas@cip.mathematik.uni-stuttgart.de;reif@mathematik.tu-darmstadt.de

  • Venue:
  • SIAM Journal on Numerical Analysis
  • Year:
  • 2010

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Abstract

We derive Sobolev-type inner products with respect to which hat functions on arbitrary triangulations of domains in $\mathbb{R}^d$ are orthogonal. Compared with linear interpolation, the resulting approximation schemes yield superior accuracy at little extra cost.