Some error estimates for the numerical approximation of surface integrals

Authors:
Kurt Georg and Johannes Tausch

Journal:
Math. Comp. **62** (1994), 755-763

MSC:
Primary 65D30

DOI:
https://doi.org/10.1090/S0025-5718-1994-1219704-1

MathSciNet review:
1219704

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Abstract: Recently, the first author introduced a new approach to the numerical quadrature of surface integrals in the context of boundary element methods. It is assumed that a global parametrization *m* of the surface is only indirectly given (e.g., via an iterative method) and that *m* is not accessible analytically. Of particular interest are parametrizations which are based on automatic triangulations of surfaces. In order to avoid an explicit reference to the partial derivatives of *m*, modified trapezoidal and midpoint rules were introduced. The present paper discusses some error estimates for these methods. The estimates are surprisingly difficult since -terms have to be shown to cancel; this does not occur in the expansion of the standard rules.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1994-1219704-1

Keywords:
Numerical surface integration,
error estimates of quadrature rules,
boundary element method,
piecewise linear surface approximation,
extrapolation method,
quadrature formula,
trapezoidal rule,
midpoint rule

Article copyright:
© Copyright 1994
American Mathematical Society