A robust Morley type conforming discontinuous galerkin method for a fourth order singular perturbation problem

Abstract We propose and analyze a robust Morley type conforming discontinuous Galerkin method for a fourth order perturbation problem. Employing the medius error analysis techniques, we carefully establish a robust error estimate assuming minimal regularity conditions. More precisely, we prove the uniform convergence with respect to the perturbation parameter for the numerical methods in the energy norm. Some numerical results are also carried out to confirm the corresponding theoretical analysis.