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Adaptive tetrahedral mesh generation by constrained centroidal voronoi‐delaunay tessellations for finite element methods
Author(s) -
Chen Jie,
Huang Yunqing,
Wang Desheng,
Xie Xiaoping
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21845
Subject(s) - voronoi diagram , delaunay triangulation , mathematics , tetrahedron , finite element method , superconvergence , centroidal voronoi tessellation , partial differential equation , constrained delaunay triangulation , adaptive mesh refinement , estimator , algorithm , mathematical optimization , geometry , mathematical analysis , computational science , statistics , physics , thermodynamics
This article presents a tetrahedral mesh adaptivity algorithm for three‐dimensional elliptic partial differential equations (PDEs) using finite element methods. The main issues involved are the mesh size and mesh quality, which have great influence on the accuracy of the numerical solution and computational cost. The first issue is addressed by a posteriori error estimator based on superconvergent gradient recovery. The second issue is solved by constrained centroidal Voronoi–Delaunay tessellations (CCVDT), which guarantees good quality tetrahedrons over a large class of mesh domains even, if the grid size varies a lot at any particular refinement level. The CCVDT enjoys the energy equidistribution property so that the errors are very well equidistributed with properly chosen sizing field (density function). And with this good property, a new refinement criteria is raised which is different from the traditional bisection refinement. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1633–1653, 2014