  Two Morley-Wang-Xu element methods with penalty for the fourth order elliptic
singular perturbation problem are proposed in this paper, including the
interior penalty Morley-Wang-Xu element method and the super penalty
Morley-Wang-Xu element method. The key idea in designing these two methods is
combining the Morley-Wang-Xu element and penalty formulation for the Laplace
operator. Robust a priori error estimates are derived under minimal regularity
assumptions on the exact solution by means of some established a posteriori
error estimates. Finally, we present some numerical results to demonstrate the
theoretical estimates.
