Coupled nonlinear advection–diffusion–reaction system for prevention of groundwater contamination by modified upwind finite volume element method

The coupled advection-dominated diffusion reaction equations arising in the prevention of groundwater contamination problem are approximated by the modified upwind finite volume element method. In order to solve the resulting nonlinear system efficiently, we use a two-grid algorithm to decompose the nonlinear system into a small nonlinear system on a coarse grid with mesh size HH and a linear system on a fine grid with mesh size hh. It is shown that the approximation still achieves asymptotically optimal as long as the mesh sizes satisfy H=O(h1/3)H=O(h1/3). Numerical examples are presented to illustrate efficiency and accuracy of the proposed method.