Abstract

. We present a novel approach to the development of a three-dimensional simplicial refinement strategies based on ideas that have been shown to be effective for two-dimensional refinement. This procedure can be applied with other refinement algorithms with minimal adjustments and can be extended recursively to even higher-dimensional spaces. keywords. mesh refinement, 3D bisection, tetrahedra, adaptivity 1 Introduction As is well known, there are two main steps in local adaptive refinement: the refinement of a subset of elements, and the achievement of the conformity of the mesh. The elements that offer the simplest choice in any dimension are the simplices: triangles in two dimensions, tetrahedra in three dimensions and their analog in even higher dimensions. There are also some algorithms based on bisection or longest-side midpoint insertion [1, 2, 3, 4, 5, 6]. 1.1 Notation and definitions Definition 1 (n-simplex) Suppose X0 ; X1 ; : : : ; Xn are n + 1 points such that the set of ve...

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