Arnold Reusken is professor of Numerical Analysis at RWTH-Aachen. His research areas are: analysis and application of multigrid techniques, finite element methods, fast iterative methods for discretized PDEs, numerical methods for two-phase incompressible flow problems. Sven Gross is a PostDoc at the Hausdorff Center for Mathematics working at the Institute for Numerical Simulation at the University of Bonn. His research interests are adaptive extended finite element methods for two-phase incompressible flows and inverse problems in the context of chemical engineering applications. He is one of the core-developers of the two-phase flow solver DROPS.

From the reviews: "This book is a first work providing an introduction to and an overview of such numerical methods. Some important and specific topics are considered in five parts of the book. ... The material is intelligible to readers with a basic knowledge of numerical treatment of one-phase flow problems. ... a basic book to researchers already working in the field of numerical simulation of two-phase flows." (Titus Petrila, Zentralblatt MATH, Vol. 1222, 2011) "This book gives a mathematically rigorous introduction to the application of finite element methods in the field of incompressible two-phase flows. ... the authors not only present an extensive literature review and a number of established results, but also identify several knowledge gaps where few results are known for two-phase flows. ... I find this book highly interesting. In particular, I strongly recommend it as preparatory reading for the Ph.D. students or young scientists in the field ... ." (Tore Flatten, Mathematical Reviews, January, 2013)

• Introduction.- Part I One-phase incompressible flows.- Mathematical models.- Finite element discretization.- Time integration.-