On optimal triangular meshes for minimizing the gradient error View Full Text


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Article Info

DATE

1991-12

AUTHORS

E. F. D'Azevedo, R. B. Simpson

ABSTRACT

Construction of optimal triangular meshes for controlling the errors in gradient estimation for piecewise linear interpolation of data functions in the plane is discussed. Using an appropriate linear coordinate transformation, rigorously optimal meshes for controlling the error in quadratic data functions are constructed. It is shown that the transformation can be generated as a curvilinear coordinate transformation for anyC data function with nonsingular Hessian matrix. Using this transformation, a construction of nearly optimal meshes for general data functions is described and the error equilibration properties of these meshes discussed. In particular, it is shown that equilibration of errors is not a sufficient condition for optimality. A comparison of meshes generated under several different criteria is made, and their equilibrating properties illustrated. More... »

PAGES

321-348

References to SciGraph publications

  • 1973. Good Approximation by Splines with Variable Knots in SPLINE FUNCTIONS AND APPROXIMATION THEORY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01385784

    DOI

    http://dx.doi.org/10.1007/bf01385784

    DIMENSIONS

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