From the constrained delaunayTriangulation object to [p, e, t]

Hello everyone. I would like to ask how can I use the constrained delaunayTriangulation object.

Let's talk about the example of US map(Example Six: Create Constrained Delaunay Triangulation of Geographical Map) from the Mathworks documentation https://de.mathworks.com/help/matlab/math/creating-and-editing-delaunay-triangulations.html

It's a non-convex geometry. We generate a constriained delaunay triangulation object, say dt, by function delaunayTriangulation. Then, it is drawn according to io=isInterior(dt) by patch('Faces',dt(io,:),'Vertices',dt.Points,'FaceColor','r'). I would like to know how can I refine the triangulation.

My idea is obtaining the triple [p,e,t] firstly, then using function refinemesh().

Actually, I would like to solve a partial differential equation based on a non-convex 2D geometry or let say a delaunayTriangulation object. Getting the triple [p,e,t] maybe a good start.