Exact Finite Element Method

In this paper, a new method, exact element method for constructing finite element, is presented.It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variable coefficient under arbitrary boundary condition.Its convergence is proved and its united formula for solving partial differential equation is given.By the present method, a noncompatible element can be obtained and the compatibility conditions between elements can be treated very easily.Comparing the exact element method with the general finite element method with the same degrees of freedom, the high convergence rate of the high order derivatives of solution can be obtained.Three numerical examples are given at the end of this paper, which indicate all results can converge to exact solution and have higher numerical precision.