Quadrature over curved surfaces by extrapolation

Lyness, J. N.

doi:10.1090/S0025-5718-1994-1257576-X

Quadrature over curved surfaces by extrapolation

Author: J. N. Lyness
Journal: Math. Comp. 63 (1994), 727-740
MSC: Primary 65D32
DOI: https://doi.org/10.1090/S0025-5718-1994-1257576-X
MathSciNet review: 1257576
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we describe and justify a method for integrating over curved surfaces. This method does not require that the Jacobian be known explicitly. This is a natural extension of extrapolation (or Romberg integration) for planar squares or triangles.

F. L. Bauer, H. Rutishauser, and E. Stiefel, New aspects in numerical quadrature, Proc. Sympos. Appl. Math., Vol. XV, Amer. Math. Soc., Providence, R.I., 1963, pp. 199–218. MR 0174177

R. Courant, Differential and integral calculus, Vol. 2, Interscience, New York, 1956.

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 a simplex, SIAM J. Numer. Anal. 15 (1978), 122-133, 870-877.

J. N. Lyness and K. K. Puri, The Euler-Maclaurin expansion for the simplex, Math. Comp. 27 (1973), 273–293. MR 375752, DOI https://doi.org/10.1090/S0025-5718-1973-0375752-1
C. Schwab and W. L. Wendland, On numerical cubatures of singular surface integrals in boundary element methods, Numer. Math. 62 (1992), no. 3, 343–369. MR 1169009, DOI https://doi.org/10.1007/BF01396234
A. H. Stroud, Approximate calculation of multiple integrals, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. Prentice-Hall Series in Automatic Computation. MR 0327006
P. Verlinden and R. Cools, Proof of a conjectured asymptotic expansion for the approximation of surface integrals, Math. Comp. 63 (1994), no. 208, 717–725. MR 1257581, DOI https://doi.org/10.1090/S0025-5718-1994-1257581-3