Daniel,
> > I'm guessing that even if something like this exists it has not been
> > implemented, but I figure this is the right community to ask..
> >
> > If I have a term in my equations that I only want to apply over part of
> > my domain, and in fact I would like the divide between the parts of the
> > domain to be able to cut through cells, is there any quadrature theory I
> > can use to evaluate the integrals involved?
> >
> > To be a little more clear; say I have a quantity \eta defined piecewise
> > bilinearly over the domain, and I want to evaluate <u,v> where \eta > 0.
So you want to integrate something like
\int \theta(\eta) u v dx
where \theta is the heaviside function. The thing to realize is that in a case
like this the integrand is no longer smooth (it may have kinks or
discontinuities where \eta changes sign) and so higher order quadrature does
not help you anything at all: you get small errors with higher order
quadrature by doing Taylor expansion of the integrand and realizing that the
error term becomes smaller as the order grows, but that doesn't work with
functions that are not smooth.
The way to go in a case like this is not to increase 'p' but to decrease 'h',
in that case the size 'h' of the cells over which you integrate and on which
the integrand is non-smooth. You can do this either by mesh refinement, or by
simply applying a low-order integration formula on sub-cells -- i.e. to use
an iterated quadrature formula. What I'd do is to use QIterated with
QGauss(2) and choose a suitable number of iterations to drive the error down.
Cheers
W.
-------------------------------------------------------------------------
Wolfgang Bangerth email: [EMAIL PROTECTED]
www: http://www.math.tamu.edu/~bangerth/
_______________________________________________
