*Red-Green* refinement is based on the bisection of all edges of a
simplex in one step. The resulting mesh topology which defines the
connectivity of the split points is chosen such that the refined elements
and the original element are self-similar. This is possible for the split
element itself (*Red* refinement) but not for the neighbor elements of
which not all edges are split (*Green* refinement).
In such a way the original geometrical element quality can be preserved,
but not improved. Hence, such a refinement is only justified when the mesh
density needs to be increased according to the control space.
The name ``Red-Green refinement'' in literature often refers to the
two-dimensional case where the simplex is a triangle.
The triangle is split into four triangles of the same shape and the
adjacent triangles are each split into two triangles. The same effect could
be accomplished with a more universal bisection technique combined with
local transformations. Only the desired edges are split. With several
adaptation steps including topological modifications the same refinement
pattern can be reached as results from the Red-Green technique.

In three dimensions Red-Green refinement with mixed elements has been investigated by [88]. Splitting all edges of the three-dimensional simplex (tetrahedron) introduces six refinement points which define an octahedron (Fig. 3.14).

The neighbor elements (Green region) form the transition from the refined area to the unrefined area. The implementation in

2000-01-20