Discrete boundary conditions for problems with interface (Q5944631)

A boundary value problem with interfaces for a second-order selfadjoint elliptic 2D-operator is considered. The solution is sought in a domain the internal boundaries of which contain only line segments having a common point. By introducing an artificial part of the boundary, for instance a circle, the singular point is separated and a boundary condition in a discrete form is derived. The obtained nonsingular problem is solved by the finite element method. Some model examples are presented.