Methods for hyperbolic systems with stiff relaxation

Three methods are analysed for solving a linear hyperbolic system that contains stiff relaxation. We show that the semi-discrete discontinuous Galerkin method, with a linear basis, is accurate when the relaxation time is unresolved (asymptotic preserving-AP). The two other methods are shown to be non-AP. To discriminate between AP and non-AP methods, we argue that in the limit of small relaxation time, one should fix the dimensionless parameters that characterize the near-equilibrium limit. Copyright (C) 2002 John Wiley Sons, Ltd.