ABSTRACT
Higher-order numerical quadrature
The numerical quadrature technique (sometimes referred to as cubature in
three spatial dimensions) lies at the heart of all higher-order nite element
codes. When evaluating the approximate variational formulation (1.22) on the
reference element, one has to numerically integrate higher-order shape func-
tions and their products, their derivatives, sometimes nonlinearities coming
from the reference maps and other higher-order terms. The order of accuracy
of the numerical integration should correspond to the highest polynomial order
that appears behind the integral sign, otherwise one risks a loss of accuracy
of the whole scheme and other disagreeable side-eects. Sometimes exact in-
tegration is not possible (e.g., because the variational formulation contains
nonpolynomial terms) { in such cases one has to be very careful and choose
the order of accuracy of the quadrature a little higher rather than a little
lower.
