Abstract: In this paper we mainly discuss the nonconforming finite element method for second order elliptic boundary value problems on anisotropic meshes.By changing the discretization form(i.e.,by use of numerical quadrature in the procedure of computing the left load),we obtain the optimal estimate O(h),which is as same as in the traditional finite element analysis when the load f∈H¹(Ω)∩C⁰(Ω)which is weaker than the previous studies.The results obtained in this paper are also valid to the conforming triangular element and nonconforming Carey’s element. 

Key words:  , Crouzeix-Raviart type, nonconforming finite elernemt, anisotropic meshes, er- ror estimate