Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws

By Huazhong Tang, Tao Tang. SIAM Journal on Numerical Analysis, 2003

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Mathematical Principles of Anisotropic Mesh Adaptation (2006, background): “It is worth mentioning that adaptation functionals for steady problems can also be used for solving time dependent problems, particularly in the context of moving meshes; see [5, 13, 36,44,51,56].”
An adaptive mesh redistribution method for nonlinear Hamilton--Jacobi equations in two-and three-dimensions (2003, methodology): “• As demonstrated in Tang and Tang [ 33 ], the mesh moving speed c can be made of order OðDnÞ .A s a result, it follows that the error of the interpolation formula (2.27) is of order OðDn2Þ.”
Adaptivity with moving grids (2009, methodology): “…and Hou (2001), Chacón and Lapenta (2006), Lapenta and Chacón (2006), Di, Li, Tang and Zhang (2005), Huang and Zhan (2004), Mackenzie and Robertson (2002), Ren and Wang (2000), Stockie et al. (2000), Tang and Tang (2003) and Zegeling and Kok (2004) on moving mesh methods and their applications.”
Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes (2006, background): “Tang and Tang [41]), although we do not pursue too far in unstructured meshes here.”