Dr. Ch. Becker To my parents

and my wife Corinna vAcknowledgments It is impossible to acknowledge everyone who directly or indirectly contributed to the realization of this thesis. I apologize to all those not mentioned by name: You have been a great help. In particular, I would like to express my sincere gratitude to the following people: Professors Dmitri Kuzmin and Stefan Turek guided my scientific career from the first contact to Numerical Mathematics to advanced topics of Computational Fluid Dynamics. I am deeply indebted to them for giving me the opportunity to work in a friendly atmosphere at the Institute of Applied Math-ematics at the ‘Technische Universität Dortmund’, formerly known as ‘University of Dortmund’. I want to thank them for supervising my scientific education during the last years; their ideas, fruitful discussions and encouraging criticisms helped me to improve my knowledge and, finally, led to the numerical methods and mesh adaptation algorithms presented in this thesis. I am very grateful to Professor Rainald Löhner for supporting me in implementing his ‘non-dimensional error indicator ’ and giving advise in adaptive mesh refinement algorithms. I am also indebted to Dr. Jaroslav Hron for sharing his experience in discrete Newton methods with me