ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991): 65B05, 65B15, 65D32
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. We present a new technique for the numerical integration over $\cal R$ , a square or triangle, of an integrand of the form $(\nabla u)^{\rm T} B (\nabla v)$ . This uses only function values of $u$ , $B$ , and $v$ , avoiding explicit differentiation, but is suitable only when the integrand function is regular over $\cal R$ . The technique is analogous to Romberg integration, since it is based on using a sequence of very simple discretizations $\mbox{\rm J}^{(m)}, m = 1,2,3,...,$ 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050320
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