Hi all, 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. The difficulty is in the cells where \eta is positive on some vertices and negative on others. I can describe algebraically the level set of \eta in those cells, and if I'm a masochist I think I can evaluate <u,v> in those cells if u and v are members of a bilinear nodal basis. (or get maple to do it for me, but there's still plenty of room for mistakes on my part.) Is there an alternative that is probably good enough? That is, might i be ok with a very high order quadrature? Or is there theory regarding quadrature on the type of domains I'm describing, maybe something approximate? I realize that these all depend highly on the problem I'm trying to solve. But I'm banking that someone has at least thought about it before - if so, I would really appreciate your thoughts.. Dan _______________________________________________
