Morley-Wang-Xu element methods with penalty for a fourth order elliptic singular perturbation problem
This work provides numerical methods for solving singularly perturbed fourth-order elliptic problems, but the contribution is incremental as it combines existing elements with penalty techniques.
The paper proposes two Morley-Wang-Xu element methods with penalty for fourth-order elliptic singular perturbation problems, achieving robust a priori error estimates under minimal regularity assumptions, validated by numerical results.
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.