Methods for hyperbolic systems with stiff relaxation

Abstract

AbstractThree 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 © 2002 John Wiley & Sons, Ltd.