Convergence analysis of carey nonconforming finite element for the second-order elliptic problem with the lowest regularity

In this paper, the Carey nonconforming finite element method (NFEM) for the second order elliptic problem is discussed. By means of the different techniques from the existing literatures, the non-uniform and uniform convergences are obtained only under the lowest regularity assumption on the solution $$ u\in {H}_0^1\left(\Omega \right). $$