We show the importance of the error function in the approximation of the solution of singularly perturbed convection-diffusion problems with discontinuous boundary conditions. It is observed that the error function (or a combination of them) provides an excellent approximation and reproduces accurately the effect of the discontinuities on the behaviour of the solution at the boundary and interior layers.

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Springer-Verlag
A.D. Fitt , J. Norbury , H. Ockendon , E. Wilson
European Conference on Mathematics for Industry

López, J. L., Pérez Sinusía, E., & Temme, N. (2010). The error function in the study of singularly perturbed convection-diffusion problems with discontinuous boundary data. In A. D. Fitt, J. Norbury, H. Ockendon, & E. Wilson (Eds.), Progress in Industrial Mathematics at ECMI 2008 (pp. 105–110). Springer-Verlag.