The Error Estimates And Numerical Simulation Of Fully Discrete Two-Step Mixed Element Method For The Symmetric Regularized Long Wave Equation

In this paper, a second-order explicit two-step scheme based on the classical mixed el-ement method are studied and discussed for the symmetric regularized long wave (SRLW) equation. The classical mixed finite element scheme is introduced in the spatial direction, then the explicit two-step difference scheme is used in the time direction.Some a priori error results of variables u and ρ in the L2-norm based on the explicit two-step fully discrete mixed element scheme are derived and analyzed, the optimal order of convergence O(△t)2+hm+1+hk+1) can be obtained. Moreover, a fully discrete a priori error analysis in the H1-norm for variable u is also made and the optimal rate of onvergence O((△t)2+hm+1+hk)is arrived at.Finally, a numerical example is chosen and some numerical results are calculated to confirm our theoretical results. From the calculating results, it is not hard to find that the numerical results keep consistent with the theoretical analysis.