Efficient second-order semi-implicit finite element method for fourth-order nonlinear diffusion equations

We focus here on a class of fourth-order parabolic equations that can be written as system second-order by introducing an auxiliary variable. design novel fully discrete mixed finite element method to approximate these equations. In our approach, we propose new techniques using the backward differentiation formula for time derivative and special technique approximation nonlinear terms. The use proposed terms makes developed numerical scheme efficient in computational cost since only deals with linear at each step no iterative resolution is needed. A convergence study performed manufactured analytical solutions where investigate different boundary conditions. With respect spatial discretization, rates are found least match priori error estimates available problems. analysis completed investigation temporal discretization numerically demonstrate time-accuracy reference solution. present series tests efficiency robustness scheme.