I'm in a undergraduate course in numerical analysis using Burden and Faires book 9th edition.
In section 12.4 about the finite element method for solving partial differential equations. They say that we should divide the boundary of the region we are studying in two pieces $S_1$ and $S_2$. We impose the boundary conditions in $S_1$. In addition $S_2$ is required to satisfy certain condition for the solution.
After reading that section twice which is the last of the book, I see no treatment about how to choose this partition of the boundary. Also, they provide a pseudo code for the finite element method and part of the input is a triangulation of the region indicating which of these triangles have sides that lie in $S_1$ or $S_2$. Finally an example is given over an irregular polygon with seven sides and they choose two (those aligned with the coordinate axis) as $S_1$ but with no indication of why they make that decision.
I would like to know if I'm missing something or if this particular division of the boundary has another name so I can look for it in another book.
Thank you.