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.
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Sign up to join this communityIn 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.
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...