Moving mesh methods are an effective, mesh-adaptation-based approach for the numerical solution of mathematical models of physical phenomena. Currently there exist three main strategies for mesh adaptation, namely, to use mesh subdivision, local high order approximation (sometimes combined with mesh subdivision), and mesh movement. The latter type of adaptive mesh method has been less well studied, both computationally and theoretically.
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. The partial differential equations considered are mainly parabolic (diffusion-dominated, rather than convection-dominated).
The extensive bibliography provides an invaluable guide to the literature in this field. Each chapter contains useful exercises. Graduate students, researchers and practitioners working in this area will benefit from this book.
Weizhang Huang is a Professor in the Department of Mathematics at the University of Kansas.
Robert D. Russell is a Professor in the Department of Mathematics at Simon Fraser University.
Applied Mathematical Sciences Volume 174 Editors S.S Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park, MD 20742-4015 USA
[email protected] J.E. Marsden Control and Dynamical Systems, 107-81 California Institute of Technology Pasadena, CA 91125 USA
[email protected] L. Sirovich Laboratory of Applied Mathematics Department of Biomathematical Sciences Mount Sinai School of Medicine New York, NY 10029-6574
[email protected] Advisors L. Greengard P. Holmes J. Keener J. Keller R. Laubenbacher B.J. Matkowsky A. Mielke C.S. Peskin K.R. Sreenivasan A. Stevens A. Stuart For other titles published in this series, go to www.springer.com/series/34 Weizhang Huang • Robert D. Russell Adaptive Moving Mesh Methods Weizhang Huang Department of Mathematics The University of Kansas Lawrence, KS 66045 USA
[email protected] Robert D. Russell Department of Mathematics Simon Fraser University Burnaby, BC V5A 1S6 Canada
[email protected] ISSN 0066-5452 ISBN 978-1-4419-7915-5 e-ISBN 978-1-4419-7916-2 DOI 10.1007/978-1-4419-7916-2 Springer New York Dordrecht Heidelberg London Mathematics Subject Classification (2010): 41A05, 41A15, 6500, 65D17, 65D18, 65K10, 65L10, 65L50, 65L60, 65M06, 65M08, 65M15, 65M20, 65M50, 65M60, 65N40, 65N50, 74S05, 74S10, 74S20, 80M10 © Springer Science+Business + Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection w