Isotropic and Anisotropic Adaptive Meshes : Models and Convergence Properties
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We review shortly two mathematical notions for mesh adaption, the order of convergence when the number of nodes is considered, and the functional model of continuous metrics. We point out the rather poor convergence properties of isotropic mesh adaption strategies, by exhibiting a barrier for the order of convergence. We show that the continuous metrics concept opens the door too an elegant derivation of optimal mesh adaption. These ideas are presented in the simplified case of mesh adaptive interpolation or compression. We dedicate this work to Professor Satofuka, expressing our admiration for the work of the scientist and our friendliness for our colleague.
KeywordsMesh Adaption Adaptive Mesh Refinement Mesh Adaptation Continuous Metrics Finite Element Interpolation
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