We establish the Harnack inequality for advection-diffusion equations with divergencefree drifts of low regularity. While our previous work [IKR] considered the elliptic case, here we treat the more challenging parabolic problem by adapting the classical Moser technique to parabolic equations with drifts with regularity lower than the scale-invariant spaces.

n this paper, we have implemented the finite element method for numerical solution of a boundary and initial value problems, mainly on solving one two-dimensional advection-diffusion equation with constant parameters. In doing so, basic idea is to first rewrite problem as variational equation, then seek approximation from space continuous piece-wise linear’s. This discretization procedure resul...

Abstract In this paper, we consider separating the discretisation of diffusive and advective fluxes in complete flux scheme. This allows combination several methods for homogeneous with (CF) method. particular, explore hybrid mimetic mixed (HMM) method CF method, order to utilise advantages each these methods. The usage HMM us handle anisotropic diffusion tensors on generic polygonal (polytopal...

Water resources worldwide require management to meet industrial, agricultural, and urban consumption needs. Management actions change the natural flow regime, which impacts the river ecosystem. Water managers are tasked with meeting water needs while mitigating ecosystem impacts. We develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, ...