Proof of a conjectured asymptotic expansion for the approximation of surface integrals
Authors:
P. Verlinden and R. Cools
Journal:
Math. Comp. 63 (1994), 717-725
MSC:
Primary 65D30
DOI:
https://doi.org/10.1090/S0025-5718-1994-1257581-3
MathSciNet review:
1257581
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Abstract | References | Similar Articles | Additional Information
Abstract: Georg introduced a new kind of trapezoidal rule and midpoint rule to approximate a surface integral over a curved triangular surface and conjectured the existence of an asymptotic expansion for this approximation as the subdivision of the surface gets finer. The purpose of this paper is to prove the conjecture.
- Kurt Georg, Approximation of integrals for boundary element methods, SIAM J. Sci. Statist. Comput. 12 (1991), no. 2, 443–453. MR 1087769, DOI https://doi.org/10.1137/0912024
- Kurt Georg and Johannes Tausch, Some error estimates for the numerical approximation of surface integrals, Math. Comp. 62 (1994), no. 206, 755–763. MR 1219704, DOI https://doi.org/10.1090/S0025-5718-1994-1219704-1
- J. N. Lyness, Quadrature over curved surfaces by extrapolation, Math. Comp. 63 (1994), no. 208, 727–740. MR 1257576, DOI https://doi.org/10.1090/S0025-5718-1994-1257576-X
- J. N. Lyness, Quadrature over a simplex. I. A representation for the integrand function, SIAM J. Numer. Anal. 15 (1978), no. 1, 122–133. MR 468118, DOI https://doi.org/10.1137/0715008
- Walter Rudin, Functional analysis, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. McGraw-Hill Series in Higher Mathematics. MR 0365062
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Additional Information
Keywords:
Numerical integration,
surface integral,
Euler-Maclaurin expansion,
boundary element method
Article copyright:
© Copyright 1994
American Mathematical Society