Asymptotic approximations for singularly perturbed convection-diffusion problems with discontinuous boundary conditions
E. Pérez Sinusía (Dpto. de Ingeniería Matemática e Informática, Universidad Pública de Navarra, Spain) and J.L. López (Dpto. de Ingeniería Matemática e Informática, Universidad Pública de Navarra, Spain)
We are interested in approximating the solution of different singularly perturbed convection-diffusion problems with discontinuous boundary conditions defined on several bounded and unbounded domains. An asymptotic expansion of the solution of these problems is obtained from an integral representation of the exact solution in the singular limit and also near the discontinuities of the boundary condition. It is observed that the error function plays a fundamental role as a basic approximant of the solution of the problems here studied and that this approximation characterizes the effect of the discontinuities on the behaviour of the solution and its derivatives in the boundary layers or the internal layers appearing in this kind of problems. We also try to value its possible application in numerical methods.