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Adaptive grid methods are among the most important classes of numerical methods for partial different equations that arise from scientific and engineering computing. The study of this type of methods has been very active in recent years for algorithm design, theoretical analysis and applications to practical computations. This volume contains a number of self-contained articles for adaptive finite element and finite difference methods, which is aimed to provide some introduction materials for graduate students and junior researchers and a collection of reference for researchers and practitioners.
The articles in this volume, which are ordered alphabetically by authors, touch upon various aspects of adaptive methods for algorithmic design, theoretical analysis and practical applications.
Chapter 1 Convergence of Adaptive Finite Element Methods
Chapter 2 A Posteriori Error Estimator by Post-processing
Chapter 3 Anisotropic Mesh Adaptation and Movement
Chapter 4 Convergence Theory of Moving Grid Methods
Chapter 5 Computation of Crystalline Microstructures with The Mesh Transformation Method
Chapter 6 On The Use of Moving Mesh Methods to Solve PDEs
Chapter 7 Theory and Application of Adaptive Moving Grid Methods
Chapter 8 Recovery Techniques in Finite Element Methods
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