Locally Adapted Tetrahedral Meshes Using Bisection

. We present an algorithm for the construction of locally adapted conformal tetrahedral meshes. The algorithm is based on bisection of tetrahedra. A new data structure is introduced, which simplifies both the selection of the refinement edge of a tetrahedron and the recursive refinement to conformity of a mesh once some tetrahedra have been bisected. We prove that repeated application of the algorithm leads to only finitely many tetrahedral shapes up to similarity, and bound the amount of additional refinement that is needed to achieve conformity. Numerical examples of the effectiveness of the algorithm are presented. 1. Introduction. The generation of locally adapted conforming tetrahedral meshes is an important component of many modern algorithms, for example, in the finite element solution of partial differential equations. Typically, such meshes are produced by starting with a coarse tetrahedral mesh, selecting certain elements for refinement, somehow refining those elements and ot..