Error Estimates Of Four Morley Type Elements For The Harmonic Equation

In this paper,we study four Morley type non-C0nonconforming finite elements for the harmonic equation,introduce respectively rectangular Morley element,cub Morley ele-ment,triangle Morley element and tetrahedron Morley element.In the rectangular Morley element and cub Morley element,we introduce the double set parameter method making the new unit have anisotropic property.Under the condition of without using Trace theorem,we develop a new technique to transform some boundary integrals to some element’s ones in the estimate of the consistency error.Furthermore we derive the optimal convergence rate is O(h).In the triangle Morley element and tetrahedron Morley element,the conventional condition judging anisotropic property is invalid.Then we introduce a new method making the new unit have anisotropic property.In addition,we make different sizes and different direction of the interpolation error a further.