Anisotropic mesh adaptation: towards user‐independent, mesh‐independent and solver‐independent CFD. Part I: general principles

By W. Habashi, J. Dompierre, Y. Bourgault, D. Ait-Ali-Yahia, Michel Fortin, M. Vallet. 2000

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Grid adaptation for functional outputs: application to two-dimensional inviscid flows (2002, methodology): “For example, a common strategy is to adapt to certain physical features of the flow, such as shock waves, boundary layers, wakes, slip lines, or stagnation points, by employing indicators based on large flow gradients [3, 5, 7 , 13, 18].”
Arbitrary Lagrangian–Eulerian Methods (2004, background): “(1996), Ait-Ali-Yahia et al. (2002), Habashi et al. (2000) and Müller (2002) for the practical implementation of such procedures.”
Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics (2011, methodology): “For spatially second-order methods, the dominant method for detecting anisotropy involves estimating the Hessian matrix H of a scalar solution u [109,111,113,123].”
A two-dimensional moving finite element method with local refinement based on a posteriori error estimates (2003, methodology): “The second and third author were supported in part by NSF grants 0209313 and DMS-007424, respectively.”
Continental scale, high order, high spatial resolution, ice sheet modeling using the Ice Sheet System Model (ISSM) (2012, methodology): “[38] Static anisotropic adaptive mesh refinement is based on the fact that interpolation-based a-priori error estimates of a finite element P1 solution (piecewise linear) depend only on its Hessian [Habashi et al., 2000] provided that the solution is regular enough.”