Adaptive Moving Mesh Methods

From the reviews: "The authors of the present monograph focus on a brand of strategies for mesh adaption on which they have been working themselves, namely so called r-adaptivity. ... It is self-contained, even usable for courses and will guide the reader to much of the current development in the field." (H. Muthsam, Monatshefte fur Mathematik, Vol. 166 (1), April, 2012) "This book is valuable for both researchers and practitioners working in adaptive moving mesh methods. It presents unified analytical tools and implementation details, and provides applications of the adaptive moving mesh methods. ... In addition, the book can be used as a textbook for an advanced course in the numerical solution of partial differential equations." (Tsu-Fen Chen, Mathematical Reviews, Issue 2012 a) "This advanced textbook on adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations (mostly of parabolic type) is aimed at graduate students and researchers in the field of scientific computing and numerical analysis. ... The book is illustrated with numerous examples, which have been implemented in Matlab." (Kai Schneider, Zentralblatt MATH, Vol. 1227, 2012) "The book's focus is on mesh generation and adaptation through mesh movement techniques ... . is completed by an extensive bibliographical list consisting of more than 300 references. ... this has helped to fill in the gap between the practitioner's moving mesh techniques and a sound theoretical background. It is highly accessible and is characterized by a very clear and readable style without sacrificing mathematical rigor and soundness. ... a precious reference for a broad community of numerical analysts as well as for computational scientists."--- (Alfio Quarteroni, SIAM Review, Vol. 53 (4), 2011)

• Preface.- Introduction.- Adaptive Mesh Movement in 1D.- Discretization of PDEs on Time-Varying Meshes.- Basic Principles of Multidimensional Mesh Adaption.- Monitor Functions.- Variational Mesh Adaptive Methods.- Velocity-Based Adaptive Methods.- Appendix: Sobolev Spaces.- Appendix: Arithmetic Mean Geometric Mean Inequality and Jensen's Inequality.- Bibliography.