Date: Aug 6, 2009 1:27 AM
Author: Bruno Luong
Subject: Re: measured boundary conditions with pde toolbox
"Doug " <email@example.com> wrote in message <firstname.lastname@example.org>...
> Hmmm, I haven't heard of Dirac-Neumann boundary conditions. In this problem I want to specify the normal derivative of the scalar field at each node on the boundary.
> Anyway, that's not the sticky part--what I'm unsure about is how to specify boundary conditions from measured data, instead of specifying them as a constant or an analytic function of coordinates.
You can't. Physically, it does not make sense to measure the flux at one point locally. You need to know the flux on the boundary *entirely*. You might assume that your flux is constant or linear by edge, but you measure it at the nodes, but you cannot assume a partial flux. Take a semaphore, you can't estimate accurately the water going out a pond by measuring the water speed at one single point (or many few of them).
Constant Neumann du/dn = g on gamma (the boundary)
<=> specify integral (du/dn.f) dx := integral g.f dx, for all f
Dirac Neuman du/dn = g delta (xi)
<=> specify integral (du/dn.f) dx := g.f(x), for all f
However you won't be able to define the above integral if you only know du/dn at the nodes (you will need to know du/dn in the edge entirely)