In a finite element formulation I have the contribution
$$
\sum_{element} \int_{element} D
\frac{\partial W}{\partial x_i}
\cdot
\frac{\partial U}{\partial x_i}
dx
$$
where U and W are vectors of some trial and test functions.
The computation of D involves terms like
$$
\frac{\partial \xi_l }{\partial x_j}
\cdot
\frac{\partial U}{\partial x_j}
\cdot
A
\frac{\partial \xi_l }{\partial x_k}
\cdot
\frac{\partial U}{\partial x_k}
$$
where $$\xi_l$$ are components of the local coordinates.
How can I get the jacobian $$\displaystyle \frac{\partial \xi }{\partial x}$$ ?
