Two‐grid method for miscible displacement problem with dispersion by finite element method of characteristics

A combined method consisting of the mixed finite element method for the pressure equation and finite element method with characteristics for the concentration equation is proposed to solve the coupled system of incompressible two‐phase flow in porous media. Two‐grid algorithm based on the Newton iteration method is developed and analyzed for the nonlinear coupled system. It is shown, both theoretically and numerically, that our schemes are efficient and achieve asymptotically optimal accuracy as long as the mesh sizes satisfy H=O(h1/2). A combined method consisting of the mixed finite element method for the pressure equation and finite element method with characteristics for the concentration equation is proposed to solve the coupled system of incompressible two‐phase flow in porous media. Two‐grid algorithm based on the Newton iteration method is developed and analyzed for the nonlinear coupled system. It is shown, both theoretically and numerically, that our schemes are efficient and achieve asymptotically optimal accuracy as long as the mesh sizes satisfy H=O(h1/2).