What Is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures

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Numerical Solution of Richards' Equation: A Review of Advances and Challenges (2017, background): “There is a traditional rule of thumb that large angles (hence aspect ratios) negatively impact approximation accuracy (Shewchuk, 2002).”
Discrete Exterior Calculus (2003, background): “See, for example, Schewchuck [2002]. We will address such computational issues in a separate work.”
Thingi10K: A Dataset of 10, 000 3D-Printing Models (2016, background): “Additional quality measures ([Shewchuk 2002; Attene 2013]) can be easily adopted.”
Variational shape approximation (2004, methodology): “Note also that this partitioning method is quite different from previous clustering techniques: we use an integrated distortion error instead of a term based on local geometric criteria such as in [KT03].”
Physics-aware Difference Graph Networks for Sparsely-Observed Dynamics (2020, background): “It is unsuitable to directly use continuous differential operators to provide local behaviors because it is hard to approximate the continuous derivatives precisely with the sparse points (Shewchuk, 2002; Amenta & Kil, 2004; Luo et al., 2009).”