Adaptive Finite Element Methods for Compressible Two-Phase Flow

In this thesis we develop, apply and analyse adaptive finite element methods with error control for compressible flow problems, focusing in particular on two-phase flow. The adaptive algorithms, aiming at quantitative error control with efficient use of computational resources, are based on a posteriori error estimates, where the error is estimated in terms of the computed solution, the local mesh-size and certain stability factors. The stability factors measure the stability properties of an associated linearized dual problem. We present analytical and computational results concerning stability factors and quantitative error control in various norms