Variational mesh adaptation II: error estimates and monitor functions

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Mathematical Principles of Anisotropic Mesh Adaptation (2006, background): “3) whereas those in [34, 38] require that the mesh satisfy the two conditions as well as the geometric condition (3.”
Approaches for generating moving adaptive meshes: location versus velocity (2003, background): “It should be pointed out that although only the equidistribution measure EP(x) is considered here, additional measures of other mesh properties such as the regularity should be included for the purpose of convergence analysis, e.g., see [ 19 ] for asymptotic analysis for the interpolation error on a”
A two-dimensional moving finite element method with local refinement based on a posteriori error estimates (2003, methodology): “Another approach worth investigating is to modify the form of the MMPDE as recently introduced in [24, 25 ].”
Adaptivity with moving grids (2009, methodology): “Then an anisotropic asymptotic bound (as N → ∞) can be obtained from the interpolation theory of Sobolev spaces (Huang and Sun 2003), namely ‖eh‖2L2(ΩP ) ≤ Cα2N− 4 n ∫ ΩP ( trace ( JT [I+α−1|H(u)|]J))2 dx + h.o.t., (2.57) where H(u) denotes the Hessian of the function u, |H(u)| = √ H(u)T H(u), and…”