Optimal error estimates of nonconforming Wilson element for nonlinear nonlocal parabolic problems

Abstract

The penalty backward Euler (BE) and 2-step backward differential formula (BDF2) fully discrete schemes are proposed for the nonlinear nonlocal parabolic problems with nonconforming Wilson element. Optimal convergence results with order O(h2+τ) and order O(h2+τ2) in a modified norm, larger than the usual broken H1-norm, are obtained directly which improve the results of order O(h+τ) and order O(h+τ2) with respect to h in the previous studies, respectively. Here, h and τ denote the mesh size and time step, respectively. Finally, some numerical results are provided to confirm the theoretical analysis.