The law of triangulation of unit disk

General Discussion
1

The triangulation of unit disk is not consistent with that of rectangular area,
for example

mesh Th=square(64,64,[-4+8x,-4+8y]),

the spatial step size is

8/64=1/8,

So the error convergence order is

log(errorh)-log(errorh/2) /log2;

However, according to the division of the circle

real r=1;
real a=0,b=0;
border C(theta=0, 2pi){x=a+rcos(theta); y=b+r*sin(theta);}
// Build the mesh from boundary
mesh Th = buildmesh(C(10));
How can we get the error convergence order without knowing the size of the spatial step?

2

Remark, the mesh size on border is 2*\pi*r / 10 so the mesh size is close to
2*\pi*r / 10. Now be careful because the border is not a circle but a polygone with 10 sides.

3

Thank you. Let me ask you another question. Can we only divide triangles? Can I use rectangular elements?

4

You can only divide triangle with trunc function but no quad element in freefem++