Red–green refinement of simplicial meshes in 𝑑 dimensions
Jörg Grande · Mathematics of Computation · 2018
The local red–green mesh refinement of consistent, simplicial meshes in d d dimensions is considered. We give a constructive solution to the green closure problem in arbitrary dimension d d . Suppose that T \mathcal {T} is a simplicial mesh and that R R is an arbitrary subset of its faces, which is refined with the Coxeter–Freudenthal–Kuhn (red) refinement rule. Green refinements of simplices S ∈ T S\in \mathcal {T} are generated to restore the consistency of the mesh using a particular placing triangulation. No new vertices are created in this process. The green refinements are consistent with the red refinement on R R , the unrefined mesh regions, and all other neighboring green refinements.