Talk:Neumann boundary condition

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The usual statement is in terms of the normal derivative on the boundary (PDE case). Is the statement in terms of grad equivalent?

Charles Matthews 20:11, 18 Jun 2004 (UTC)

Which Neumann[edit]

does this kind of conditions take its name from? David.Monniaux 14:26, 22 May 2005 (UTC)[reply]

Quite likely, if not certainly, John von Neumann. Oleg Alexandrov 15:20, 22 May 2005 (UTC)[reply]

Mmmh. In keeping with the usual way of naming schemes in English, wouldn't that be Von Neumann boundary conditions? As in: Von Neumann architecture? David.Monniaux 05:11, 25 May 2005 (UTC)[reply]

Well, try to correct your fellow mathematician about that. He will resist tooth and nail. In math we have Neumann boundary conditions, Dirichlet boundary conditions, and mixed boundary conditions. They were called so for ages, and nobody would be willing to have change anything about this. Oleg Alexandrov 15:29, 25 May 2005 (UTC)[reply]

It's 19th century, not John von Neumann. Charles Matthews 07:49, 24 September 2005 (UTC)[reply]

I guess Carl Gottfried Neumann (1832-1925). Charles Matthews 07:54, 24 September 2005 (UTC)[reply]

That is, Carl Neumann, same as the guy with the Neumann series. Oleg Alexandrov 16:17, 24 September 2005 (UTC)[reply]

it was Franz Ernst Christian Neumann (1798-1895)

Concerning this edit, note that I am not sure if he is the right Neumann. Right above, somebody wrote Franz Ernst Christian Neumann. Should we write in the article info we are not sure about, or not? Oleg Alexandrov (talk) 04:03, 14 February 2006 (UTC)[reply]

I reverted my edit. I don't have any more information than anyone else, I was just trying to be bold :-). ―BenFrantzDale 04:31, 14 February 2006 (UTC)[reply]

After reading this and this, I would rather expect it was Franz Ernst Neumann (without "Christian"?) if it was not Carl Neumann (his son and the brother of Franz Ernst Christian Neumann (1834-1918)). I will try to find a reference for this (nag me if I forget it). Kusma (討論) 04:59, 14 February 2006 (UTC)[reply]

Okay, most of my PDE books don't even try to answer the question. "Maximum principles in differential equations" by Protter and Weinberger at least mentions C. Neumann in relation with the "Neumann function" (the Green's function for the Laplace operator with homogeneous Neumann conditions) and in connection with showing something about the normal derivative of the Green's function. A search in Google scholar gives these lecture notes claiming it was Carl and not his father. I think we can assume it is Carl, but I wouldn't bet my head on it. Kusma (討論) 21:17, 14 February 2006 (UTC)[reply]

I have put it into the article. I have checked a couple more PDE books and all that mentioned a name at all gave Carl's. (Most didn't mention a name). That and somebody claiming (see my last post) that it wasn't his father is enough for me until somebody comes and finds a reference that shows the contrary. Kusma (討論) 22:45, 15 February 2006 (UTC)[reply]

Thanks, it is nice to have that figured out. Oleg Alexandrov (talk) 01:35, 16 February 2006 (UTC)[reply]

Nice work. I'd swear I was told the wrong one (von) in my Heat Transfer course. ―BenFrantzDale 02:07, 16 February 2006 (UTC)[reply]

It is definitely Carl Gottfried Neumann (1832-1925) - I have added a reference to a very through paper by Cheng and Cheng (2005) detailing the history of boundary elements. Griffgruff (talk) 23:35, 4 January 2008 (UTC)[reply]

RE Neumann and third-type[edit]

Can somebody check this please. My understanding is that dirichlet is the first type, Neumann is the second type (not third) and Robin or mixed is the third type134.148.20.3 08:51, 4 September 2006 (UTC)[reply]

I was under this impression too.

Type 1 = Dirichlet, value at boundary is constant [1]
Type 2 = Neumann, derivative of value at boundary is constant [2]
Type 3 = Cauchy, weighted average of type 1 and 2 is constant [3]

--24.208.154.48 13:05, 5 December 2006 (UTC)[reply]

You are both correct! I have added a reference to this in the article. Griffgruff (talk) 23:36, 4 January 2008 (UTC)[reply]

Second Sentence?[edit]

Is there some reason for the obscurity of the second sentence: "...the condition specifies the values in which the derivative of a solution is applied within the boundary of the domain"? Is it meant to convey something different from "...the condition specifies the values for the derivative of a solution on the boundary of the domain"? I understand there are subtleties (specifies a constant value; specifies the gradient normal to the boundary), but I don't understand the sentence as is and don't see that it more correctly describes the concept than the simpler formulation. Mark Durst (talk) 22:32, 3 February 2021 (UTC)[reply]