Homogenization of Singularly Perturbed Diffusion-Advection-Reaction Equations on Periodic Networks

The numerical solution of differential equations on large periodic networks with highly oscillating coefficients is still challenging mathematics. Two-scale asymptotic methods from homogenization theory can be applied in order to obtain approximating macroscopic models. We demonstrate the effectiveness of this approach at the example of singularly perturbed diffusion-advection-reaction equations on one-dimensional manifolds.