Constrained CVT meshes and a comparison of triangular mesh generators
Computational Geometry: Theory and Applications
Adaptive finite element methods for elliptic equations over hierarchical T-meshes
Journal of Computational and Applied Mathematics
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab
Structural and Multidisciplinary Optimization
An adaptive edge finite element method for electromagnetic cloaking simulation
Journal of Computational Physics
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A new triangular mesh adaptivity algorithm for elliptic PDEs that combines a posteriori error estimation with centroidal Voronoi-Delaunay tessellations of domains in two dimensions is proposed and tested. The ability of the first ingredient to detect local regions of large error and the ability of the second ingredient to generate superior unstructured grids result in a mesh adaptivity algorithm that has several very desirable features, including the following. Errors are very well equidistributed over the triangles; at all levels of refinement, the triangles remain very well shaped, even if the grid size at any particular refinement level, when viewed globally, varies by several orders of magnitude; and the convergence rates achieved are the best obtainable using piecewise linear finite elements. This methodology can be easily extended to higher-order finite element approximations or mixed finite element formulations although only the linear approximation is considered in this paper.