Toward a universal adaptive finite element strategy part 3. design of meshes

Error Estimation and Adaptive Mesh Refinement for Aerodynamic Flows

“…The optimal refinement of κ is then chosen to be the one which leads to the smallest projection error; elements in the mesh are then refined based on those that will lead to the greatest decrease in the projection error per degree of freedom. This strategy was first introduced by Rachowicz et al [96]; see also [32,101] for more recent work.…”

“…In order to determine the optimal refinement, stimulated by the articles [96,98], we propose the following strategy based on choosing the most competitive subdivision of κ from a series of trial refinements, whereby an approximate local error indicator on each trial patch is determined. Algorithm 5.1 Given an element κ in the computational mesh T h (which has been marked for refinement), we first construct the mesh patches T h,i , i = 1, 2, 3, based on refining κ according to Figures 30(a), (b), & (c), respectively.…”

Convergence, adaptive refinement, and scaling in 1D peridynamics

“…[1,2]). Automatic and goal-oriented h, p, and hp-adaptive strategies for FEM have been introduced and discussed in [3][4][5][6].…”

Modeling and Computational Analysis of Multiscale Phenomena in Fluid-Structure Interaction Problems

“…A general approach to hp-adaptive methods was developed in a series of papers by Oden, Demkowicz, Rachowicz, and others, see [41][42][43]. There a general data structure, constructed on quadrilateral or hexahedral meshes, was developed which provided for irregular h refinements and p enrichments.…”