I know where Dirichlet and Neumann boundary conditions come from, but where do Wentzel boundary conditions arise? If my governing equation is a second-order elliptic PDE, where can a Wentzel boundary condition arise? Can you give me a specific example which I can see this boundary condition?
Also, what is the correct way to write Wentzel on research papers? I saw different spellings for this word.
Thank you.
In the 1959 paper "On boundary conditions for multidimensional diffusion processes" where he discusses this type of boundary conditions, his name is spelled Venttsel'. I presume he is Russian, so there is no unique way to write his name with the Latin alphabet, the spelling is unique only in Cyrillic. In his case I've seen already at least 5 different ways to spell his name and there might be more.
These boundary conditions arose first in probability theory. Check also this paper:
G. R. Goldstein. Derivation and physical interpretation of general boundary conditions.
These type of boundary conditions appear also in asymptotic models. Here is an explanation I found in this paper:
V. Bonnaillie-Noel, M. Dambrine, F. Herau, G. Vial.
On generalized Ventcel’s type boundary conditions for Laplace operator in a bounded domain
"In various situations, an artificial boundary condition is introduced to replace the effect of a more complex geometry. We can mention the approximate boundary conditions in the framework of thin layers or rough boundaries. For exterior problems, absorbing (or transparent) conditions are another example. These boundary conditions are generally simple differential conditions obtained from an asymptotic analysis with respect to a characteristic length: the thickness of the layer, the scale of the roughness, the diameter of the artificial boundary, for the previous three examples respectively."