# What are difference among natural boundary, exit boundary, regular boundary and killing boundary??

In the paper i'm reading, they used the terminologies, natural boundary, exit boundary, regular boundary and killing boundary.

I can't find the difference of them and definition of them.

Tell me about them or relevant reference.

• Perhaps you could cite the paper you are reading, so that Readers can better respond to your request? May 25, 2015 at 0:31

## 1 Answer

A partial answer, but perhaps others will contribute...

"The essential boundary conditions are imposed on the functions in the space where the minimzation of the energy functional is made or the weak formulation is posed. For the standard FE formulation for the Poisson equation these are Dirischlet boundary conditions. However, if one uses the dual mixed formulation, then the Dirichlet data become essentail while the Neumann BC are imposed on the flux variable which now is an independent unknown variable, this excatly what Stefano Micheletti is saying. Practically, to determine whether a BC is natural or essential, one can do the following: To get the weak form you do some integration by parts (or Stokes theorem); during this integration by parts process you need to deal with the boundary terms; then: (a) if you use the BC to produce some new terms in the bilinear and linear forms, these are natural BC; (b) if you need to elliminated them from the forms, you impose them on the functions of the space and then these are essential." - Lazarov

There are more explanations there, but I found this to be the most helpful.

Also, Feller's 1952 text might help...

• I know, but perhaps it will give pointers for others?
– ell
May 24, 2015 at 23:48
• You added 13 lines of text and a link to your question after reading my comment. Seeing that your post is now 14 lines long, I fail to see what you're even trying to argue about.
– user228113
May 24, 2015 at 23:55
• (obviously I meant "post" instead of "question").
– user228113
May 25, 2015 at 0:02