Re: Laplace equation with gradient boundary conditions
- To: mathgroup at smc.vnet.net
- Subject: [mg123304] Re: Laplace equation with gradient boundary conditions
- From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
- Date: Thu, 1 Dec 2011 05:49:33 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201111291203.HAA05406@smc.vnet.net>
On Tue, 29 Nov 2011, Tom Wolander wrote: > I have bought Mathematica 8 a week ago and this is my first post on > this board. > My main purpose for the purchase was to work on PDEs, specifically on > the heat equation. > As one of the first tests I wanted to solve a steady state temperaure > distribution on a rectangular domain with a radiative boundary > condition on one face (flux=0 on the other 3). I made sure to have > continuity in corners. > This is a rather easy exercice of a radiating wall - I have solved > many of similar and more complex problems "by hand" many years ago. > Unfortunately I failed with NDSolve in Mathematica and the tutorials > are of no help despite some 4 hours I spent in there. > I found only one rather esotherical hint somewhere deep in one "Issue" > section on a command which seemed to say that NDSolve could work only > with Cauchy boundary conditions. > If this were true, then use of Mathematica 8 would be excluded for > virtually any work in thermics where the boundary conditions are > always of the (non Cauchy) convection/radiation type. Tom, could you be a little more specific in writing down the boundary condition you want? I assume it is not a generalized Neumann condition. Is it more like a Sommerfeld condition? Thanks, Oliver > In other words the elementary steady state problem (Laplace equation) > with flux conditions on boundaries can't be solved? > > It might be that this issue has been already discussed but I couldn't > find a relevant thread by using search. > > Could somebody help me by answering whether Laplace equation with > Robin like BC can't really be solved? > And if it can be done, what have I missed to make NDSolve work? > >