Thank you very much for showing this identity @kamensky! I’ll be sure to read through the notes you wrote too. In order for me to write this on FEniCS, I’d like to hear from you if I’m guessing it right. I believe I should thus solve the following problem
- \int_\Omega (\rho \omega ^2 \mathbf{v} \cdot \mathbf{U})d \mathbf{x} -\int_\Omega(\nabla\cdot\pmb{\sigma})\cdot\mathbf{v}\,d\mathbf{x} = 0
which becomes
\int_{\Omega} (-\rho \omega ^2 \mathbf{v} \cdot \mathbf{U} + \pmb{\sigma}:\nabla\mathbf{v} )\,d\mathbf{x} = \int_{\partial\Omega}(\pmb{\sigma}\mathbf{n})\cdot\mathbf{v}\,d\mathbf{s}\text{ .}
Is this right?