A Moving Mesh Finite Element Algorithm for Singular Problems in Two and Three Space Dimensions

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An adaptive mesh redistribution method for nonlinear Hamilton--Jacobi equations in two-and three-dimensions (2003, background): “In a recent work [23], we were able to carry out some 3D simulations for some simple nonlinear problems (one scalar and one system).”
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].”
Relu Deep Neural Networks and Linear Finite Elements (2018, background): “This approach proves to be effective in many applications, see [36,37].”
Adaptivity with moving grids (2009, background): “See, for example, Adjerid and Flaherty (1986), Baines et al. (2005), Beckett et al. (2001a), Cao, Huang and Russell (1999a), Carlson and Miller (1998a, 1998b), Di et al. (2005), Lang et al. (2003), Li et al. (2002) and Wathen and Baines (1985).”
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws (2003, methodology): “Following Li, Tang, and Zhang [21] we propose a moving mesh method containing two separate parts: PDE time-evolution and mesh-redistribution.”