A Morley Type Triangular Finite Element with High Convergence for the Biharmonic Problem

In this work, we construct a theoretical framework to develop non C0 Morley type nonconforming high-convergence elements for biharmonic problems. For each element domain, P3 should be included in the space of shape functions. Besides the degrees of freedom of Morley elements, we add the integrals and first-order moments of the normal derivatives on edges. The choice of degrees of freedom and shape function space guarantees the possibility of improving the convergence order. As an application, we specifically construct a Morley type element on triangular meshes. Lastly, numerical experiments are carried out to verify the feasibility of the element.