A Weak Compatibility Condition for Newest Vertex Bisection in any dimension

We define a weak compatibility condition for the Newest Vertex Bisection algorithm on simplex grids of any dimension and show that using this condition the iterative algorithm terminates successfully. Additionally we provide an O(n) algorithm that renumbers any simplex grid to fulfil this condition. Furthermore we conduct experiments to estimate the distance to the standard compatibility and also the geometric quality of the produced meshes.