Abstract
In this work we present a survey of some geometric results on tetrahedral partitions and their refinements in a unified manner. They can be used for mesh generation and adaptivity in practical calculations by the finite element method (FEM), and also in theoretical finite element (FE) analysis. Special emphasis is laid on the correspondence between relevant results and terminology used in FE computations, and those established in the area of discrete and computational geometry (DCG).
Keywords: finite element method, tetrahedron, polyhedral domain, linear finite element, angle and ball conditions, convergence rate, mesh regularity, discrete maximum principle, mesh adaptivity, red, green and yellow refinements, bisection algorithm
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