# How can FDTD be divergence free when approximating co-located points of E and H on the Yee cell?

I am using this source as a means to produce a 3D FDTD code which can handle anisotropic material. Because tensors are used, all components of the $$E$$ and $$H$$ fields must be used when calculating the next time step of the electric field.

And because of this, approximations must be used to calculate each component of $$E$$ and $$H$$.

For instance when solving for $$E_z|^{n}_{i,j,k+1/2}$$ - then the following components are also needed.

$$E_x|^{n}_{i,j,k+1/2}$$ $$E_y|^{n}_{i,j,k+1/2}$$ $$H_x|^{n}_{i,j,k+1/2}$$ $$H_y|^{n}_{i,j,k+1/2}$$ $$H_z|^{n}_{i,j,k+1/2}$$

However none of the above co-located components are available on the Yee cell, and must be approximated

But according to this source (at time 5:40 going forward), colocated points then violate the divergence free condition. I'm then confused as how to approach coding this problem up, or why the authors of the first source would want to approximate at co-located points.