Cubature of Integrands Containing Derivatives

Lyness JN, Rüde U (1998)

Publication Type: Journal article

Publication year: 1998


Publisher: Springer Verlag (Germany)

Book Volume: 78

Pages Range: 439--461


We present a new technique for the numerical integration over ℛ, a square or triangle, of an integrand of the form (∇u)TB(∇v). This uses only function values of u, B, and v, avoiding explicit differentiation, but is suitable only when the integrand function is regular over ℛ. The technique is analogous to Romberg integration, since it is based on using a sequence of very simple discretizations J(m), m = 1,2,3, ..., of the required integral and applying extrapolation in m to provide closer approximations. A general approach to the problem of constructing discretizations is given. We provide specific cost-effective discretizations satisfying familiar, but somewhat arbitrary guidelines. As in Romberg integration, when each component function in the integrand is a polynomial, this technique leads to an exact result.

Authors with CRIS profile

How to cite


Lyness, J.N., & Rüde, U. (1998). Cubature of Integrands Containing Derivatives. Numerische Mathematik, 78, 439--461.


Lyness, J. N., and Ulrich Rüde. "Cubature of Integrands Containing Derivatives." Numerische Mathematik 78 (1998): 439--461.

BibTeX: Download