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Adaptive Moving Mesh Methods
English
145 b
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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.
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