A TWO-GRID MULTIPOINT FLUX MIXED FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC PROBLEMS

This paper introduces a two-grid multipoint flux mixed finite element (MFMFE) method for solving nonlinear parabolic problems. The MFMFE method is advantageous due to its ability to decouple saddle point algebraic systems. The two-grid algorithm transforms nonlinear problems into smaller nonlinear systems on coarse grids and linear problems on fine grids, facilitating rapid decoupling of nonlinear equations. We present semi-discrete and fully discrete backward Euler schemes for the model problem. Theoretical results demonstrate the convergence order of velocity and pressure. A numerical example validates the effectiveness of the proposed algorithm, showing that the two-grid MFMFE method significantly reduces CPU running time compared to the standard MFMFE method.