On a bisection algorithm that produces conforming locally refined simplicial meshes

First we introduce a mesh density function that is used to define a criterion to decide, where a simplicial mesh should be fine (dense) and where it should be coarse. Further, we propose a new bisection algorithm that chooses for bisection an edge in a given mesh associated with the maximum value of the criterion function. Dividing this edge at its midpoint, we correspondingly bisect all simplices sharing this edge. Repeating this process, we construct a sequence of conforming nested simplicial meshes whose shape is determined by the mesh density function. We prove that the corresponding mesh size of the sequence tends to zero for d∈=∈2, 3 as the bisection algorithm proceeds. It is also demonstrated numerically that the algorithm seems to produce only a finite number of similarity-distinct triangles.