Mesh Refinement

Mesh refinement is accomplished through edge splitting. In 2-D, an edge is incident to either one or two triangles (boundary edges and internal edges, respectively). To split the edge, we insert a node at the midpoint of the edge. The midpoint is connected to the opposite nodes of the incident triangles. In the figure below we split an internal edge.

In 3-D, an edge is incident to one or more tetrahedra. To split the edge, we insert a node at the midpoint of the edge. The midpoint is connected to each of the nodes of the incident tetrahedra which are not incident to the edge being split. (If the edge is incident to tetrahedra, the the midpoint of the split node is incident to tetrahedra.) In the figure below we split an edge of a tetrahedron.