I apologise if the formula is not correct, I found it in an article. I have trouble understanding how the chain rule is used and how this formula is obtained. Thank you!
\begin{align} &\nabla u \cdot \big [a(J_h+J_h^T)- \operatorname{div} (ah)I\big ]\nabla v=-(h\cdot \nabla u) \operatorname{div} (a\nabla v)- (h\cdot \nabla v) \operatorname{div} (a\nabla u)+\operatorname{div} \big [a(h\cdot \nabla u)\nabla v+(h\cdot\nabla v)(a\nabla u) -(a\nabla u\cdot \nabla v)h\big ] \end{align} $u,v:\mathbb{R}^2\rightarrow \mathbb{R}, h:\mathbb{R}^2 \rightarrow \mathbb{R}^2,$ a is actually $aI$ where I is the identity matrix of order 2.