I have a positive matrix $\rho \in \mathbb{R}^{n,n}_+$ as a discrete probability density. Furthermore, I have a tensor $u \in \mathbb{R}^{n,n,2}$ that is constant in time and acts as a vector field. I want to transport the mass of $\rho$ along the discrete vector field $u$ with numpy. But I am not sure how to do this or where to start.

Edit: I guess, that the convection equation with discontinuous Galerkin method might work.


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