A Nonconforming Scheme With Piecewise Quasi Three Order Polynomial Space To Solve Biharmonic Problem

A C~0 nonconforming quasi three degree element with 13 freedoms is constructed to solve biharmonic problems where the shape functions consist of polynomial space P3 and some bubble functions.13 freedoms of the C0 nonconforrming quasi three degree element are:unit,s vertices,edges' trisection points?barycenter and normal derivative integral along the edges.As the finite elements are not affine equivalent,the interpolation error estimation is proved with the help of introducing another affine finite elements.Applied the space t.o solve biharmonic problems,the error between true solution and discrete solution is of first order convergence.Numerical examples which are present,ed further illustrate the convergence analysis.