Abstract
Abstract For the purpose of finite element computation for 2D or 3D geometry, one needs an appropriate mesh of the considered domain. A class of full automatic methods, derived from Voronoi's theory, is suitable to generate the mesh of any shape via a set of points which describes the geometry. Such methods providing triangles in 2D and tetrahedra in 3D can be seen, after an adequate initialization, as the merger of each given point in an existing mesh using an updating process. Unfortunately, this mesh which contains all the given points does not contain, in general, the edges (or the faces) of the boundary which are the natural data to be satisfied. The aim of this paper is, after a brief survey of the different steps of the above method, to point out the problem of the exact fitting of the given boundary and to present a method which guarantees this crucial property.
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