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＜電子ブック＞
Adaptive Moving Mesh Methods / by Weizhang Huang, Robert D. Russell
(Applied Mathematical Sciences. ISSN:2196968X ; 174)

版	1st ed. 2011.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2011
本文言語	英語
大きさ	XVIII, 434 p : online resource
著者標目	*Huang, Weizhang author Russell, Robert D author SpringerLink (Online service)
件　名	LCSH:Numerical analysis LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Differential equations FREE:Numerical Analysis FREE:Computational Mathematics and Numerical Analysis FREE:Differential Equations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4419-7916-2

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