Difference between "DG" and "CG"?

mathematics
1

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”?

2

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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3

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.

4

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

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