Narrow Hermite Triangular Element For Second Order Problems

In this paper,a new narrow Hermite triangular element for the second order problem is constructed. Its anisotropic interpolation property for H1( )is proved, that is ,it is affine - equivalent and satisfies the conditionThe continuity of corresponding linear functionals is tested. Using the anisotropic interpolation theorems for narrow triangular finite element,the error estimte is obtained , the convergence of the second order problem is proved without the regularity condition., Meanwhile, we prove that this new element also has the anisotropic interpolation property for H2( ),and obtain the interpolation error of seminorm on H2().