Adaptive Moving Mesh Methods [Hardcover]

This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems.? Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. Graduate students, researchers and practitioners working in this area will benefit from this book.

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This book covers adaptive mesh generation and moving mesh methods for solving time-dependent PDEs. It gives a general description of the components of moving mesh methods as well as examples of their application for a number of nontrivial physical problems.?

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.

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 f?r 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 advlC=