Difference between "DG" and "CG"?

I saw the answer P and CG but didn’t get the answer. And the Jacobian of transforming a standard element to a physical element is computed using “DG” rather than “CG”, actually “CG” will give wrong results here. I am wondering why cannot “CG” element while “DG” can get the Jacobian and what are the differences between “CG” and “DG”?

CG encodes continuity between elements. (This the C, which stands for continuous)

The jacobian is defined per element. (If you look at non affine elements it is actually a non-constant function on each element).

For linear simplices (triangles and tetrahedrons) the jacobian is constant per cell

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Thanks! After searching the web and GPT stuff, I still cannot find any formal definition about CG, could you send me some info about it? Websites, books, or blogs will all be helpful.

or section 3.3 of: https://fenicsproject.org/pub/book/book/fenics-book-2011-06-14.pdf

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