Based on Ilian's comment, but modified to fit your situation.
Needs["NDSolve`FEM`"];
mesh = ToElementMesh[Disk[]];
mesh["Coordinates"] // Length
1001
Based on Ilian's comment, but modified to fit your situation.
Needs["NDSolve`FEM`"];
mesh = ToElementMesh[Disk[]];
mesh["Coordinates"] // Length
1001