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Two Morley-Wang-Xu element methods with penalty for the fourth order ellipticsingular perturbation problem are proposed in this paper, including theinterior penalty Morley-Wang-Xu element method and the super penaltyMorley-Wang-Xu element method. The key idea in designing these two methods iscombining the Morley-Wang-Xu element and penalty formulation for the Laplaceoperator. Robust a priori error estimates are derived under minimal regularityassumptions on the exact solution by means of some established a posteriorierror estimates. Finally, we present some numerical results to demonstrate thetheoretical estimates.

Morley-Wang-Xu element methods with penalty for a fourth order elliptic singular perturbation problem