A three-dimensional elliptic singular perturbation problem with discontinuous boundary values is considered. The solution of the problem is written in terms of a double integral. A saddle point analysis is used to obtain a first approximation, which is expressed in terms of a function that can be viewed as a generalization of the complementary error function

CWI
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

López, J. L., Pérez Sinusía, E., & Temme, N. (2005). First order approximation of an elliptic 3D singular perturbation problem. Modelling, Analysis and Simulation [MAS]. CWI.