Coordinates of mesh generated by Mathematica-FEM

Question

MeshCoordinates function yields more nodal coordinates than expected. Can I extract the coordinates of vertices only. Here is an example of a square region with a course mesh to explain the problem. I would like the code get me the following coordinates:{{0., 0.}, {0., 0.5}, {0., 1.}, {0.5, 0.}, {0.5, 0.5}, {0.5, 1.}, {1.,0.}, {1., 0.5}, {1., 1.}}.

Needs["NDSolve`FEM`"]
d = Rectangle[{0, 0}, {1, 1}];
mesh = ToElementMesh[d2, MaxCellMeasure -> 0.5];
mesh["Wireframe"]
MeshCoordinates[mesh2][[1, 1]]

Answer 1

The function MeshCoordinates works for MeshRegion. ToElementMesh, however, returns an ElementMesh. For an ElementMesh you can extract the coordinates in the following manner:

Needs["NDSolve`FEM`"]
d = Rectangle[{0, 0}, {1, 1}];
mesh = ToElementMesh[d2, MaxCellMeasure -> 0.5];
mesh["Wireframe"]
mesh["Coordinates"]

If you want a first order mesh use:

mesh = ToElementMesh[d2, MaxCellMeasure -> 0.5,"MeshOrder"->1];

Also, I encourage you to look at the documentation of ToElementMesh and ElementMesh for more information.