Basic Principles of Multidimensional Mesh Adaptation

We have seen in Chapter 2 the crucial role that the equidistribution principle plays in designing adaptive mesh algorithms, where in fact a mesh can be fully determined from it in 1D. The situation becomes much more complicated in multidimensions. The equidistribution principle, specifying only the volume of mesh elements, is no longer sufficient for determining a multidimensional mesh. An additional condition is needed for specifying the shape and orientation of mesh elements.