Talk:Nonlinear finite elements/Weak form of heat equation

Hi,

Shouldn't it be $$\rho C_p \frac{\partial T}{\partial t}$$ instead of $$\rho C_v \frac{\partial T}{\partial t}$$? ($$C_p$$ is the heat capacity at constant pressure while $$C_v$$ is at constant volume. I assume the two dependent variables are pressure and temperature here, not volume and temperature.

Hello, I'd strongly suggest using different notation for vectors (vector functions) and tensors. I assume kappa to be a tensor. Otherwise the first identity cannot be applied to eq. 29. Changing notation would make the example way more readable. Furthermore, Eq. 30 does not constitute a substitution but rather integration over $$V$$ in $$\Omega$$. Substitution takes place later, in Eq. 33.