Divergence

Divergence measures how vectors are converging or diverging at a given point. It is measured as the dot product between the Gradient and the vector $\vec{u}$.

$$\nabla \cdot \vec{u}$$

If divergence is positive, it’s a source (pushing stuff “out”). If it’s negative, it’s a sink.

Laplace operator

The Laplacian is the divergence of the gradient. For a vector $\vec{u}$ it is represented by $\Delta \vec{u}$ or ${\nabla }^2\vec{u}$ and equals $\nabla \cdot \nabla \vec{u}$.