Adaptive finite element methods for compressible two-phase flow

We apply the adaptive streamline diffusion method for compressible flow in conservation variables using P1 × P0 finite elements to a conservative model of two-phase flow. The adaptive algorithm is based on an a posteriori error estimate involving certain stability factors related to a linearized dual problem. For a model problem we prove that the stability factors are bounded. We compute the stability factors for some numerical examples in one- and two-space dimensions