Date: Aug 6, 2009 1:27 AM
Author: Bruno Luong
Subject: Re: measured boundary conditions with pde toolbox

"Doug " <> wrote in message <h5daso$lqr$>...
> 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.
> --Doug

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)