The coupling of hyperbolic and elliptic boundary value problems with variable coefficients

We consider a one-dimensional coupled problem for elliptic second-order ODE s with natural transmission conditions. In one subinterval, the coefficient epsilon > 0 of the second derivative tends to zero. Then the equation beco mes there hyperbolic and the natural transmission conditions are not fulfil led anymore. The solution of the degenerate coupled problem with a Bur tran smission condition is corrected by an internal boundary layer term taking i nto account the viscosity epsilon. By using singular perturbation technique s, we show that the remainders in our first-order asymptotic expansion conv erge to zero uniformly. Our analysis provides an a posteriori correction pr ocedure for the numerical treatment of exterior viscous compressible flow p roblems with coupled Navier-Stokes/Euler models. Copyright (C) 2000 John Wi ley & Sons, Ltd.