(untitled) (Advances in Applied Mathematics and Mechanics, 2022)
In this paper, a two-grid block-centered finite difference method for the incompressible miscible displacement in porous medium is introduced and analyzed, which is to solve a nonlinear equation on coarse mesh space of size H and a linear equation on fine grid of size h. We establish the full discrete two-grid block-centered finite difference scheme on a uniform grid. The error estimates for the pressure, Darcy velocity, concentration variables are derived, which show that the discrete L_2 error is O(∆t+h^2+H^4 ). Finally, two numerical examples are provided to demonstrate the effectiveness and accuracy of our algorithm.