On the Error Estimate for the Isoparametric Finite Element Method

In this paper, the isoparametric element of 2-degree Lagrange type for second order elliptic P.D.E, with nonhomogeneous Dirichlet boundary value is considered. We prove $|u-u_h|_{1,Omega}=O(h^2)$, which is the same as $|u-u_h|_{1,Omega_h}=O(h^2)$ where $Omega$ and $Omega_h$ in $R^2$ are the domain of the boundary value problem and isoparametric triangulation domain respectively.