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Adaptive Moving Mesh Methods (Applied Mathematical Sciences)by Weizhang Huang
Synopses & Reviews
The book is about adaptive mesh generation and moving mesh methods for solving time-dependent PDEs. It gives a general description of the components of moving mesh methods and gives examples of their application for a number of nontrivial physical problems. Detailed description of and analysis of how to choose optimal monitor functions for mesh generation, and the resulting optimal solution error bounds, are given. In higher dimensions this is done for finite element methods, but discretizations of differential equations for moving meshes are given for finite difference methods as well. Higher dimensional mesh generation, described in terms of mesh equidistribution and mesh alignment, allows for an interpretation of virtually all of the many variational mesh generation methods within a common framework.
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.
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.
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,
Table of Contents
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.
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