A comparison of adaptive refinement techniques for elliptic problems
ACM Transactions on Mathematical Software (TOMS)
On the maximum angle condition for linear tetrahedral elements
SIAM Journal on Numerical Analysis
On the difficulty of triangulating three-dimensional nonconvex polyhedra.
Discrete & Computational Geometry
Automatic mesh generator with specified boundary
Computer Methods in Applied Mechanics and Engineering
A comparison of tetrahedron quality measures
Finite Elements in Analysis and Design
On the shape of tetrahedra from bisection
Mathematics of Computation
A recursive approach to local mesh refinement in two and three dimensions
Journal of Computational and Applied Mathematics
Quality local refinement of tetrahedral meshes based on bisection
SIAM Journal on Scientific Computing
The 4-triangles longest-side partition of triangles and linear refinement algorithms
Mathematics of Computation
A 3D refinement/derefinement algorithm for solving evolution problems
Applied Numerical Mathematics - Special issue on numerical grid generation-technologies for advanced simulations
3D anisotropic mesh refinement in compliance with a general metric specification
Finite Elements in Analysis and Design
Acute Type Refinements of Tetrahedral Partitions of Polyhedral Domains
SIAM Journal on Numerical Analysis
Mesh quality improvement and other properties in the four-triangles longest-edge partition
Computer Aided Geometric Design
The propagation problem in longest-edge refinement
Finite Elements in Analysis and Design
Refinement based on longest-edge and self-similar four-triangle partitions
Mathematics and Computers in Simulation
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A tetrahedron t is said to be a right-type tetrahedron, if its four faces are right triangles. For any right-type initial tetrahedron t, the iterative 8-tetrahedra longest-edge partition of t yields into a sequence of right-type tetrahedra. At most only three dissimilar tetrahedra are generated and hence the non-degeneracy of the meshes is simply proved. These meshes are of acute type and then satisfy trivially the maximum angle condition. All these properties are highly favorable in finite element analysis. Furthermore, since a right prism can be subdivided into six right-type tetrahedra, the combination of hexahedral meshes and right tetrahedral meshes is straightforward.