A New Mixed Finite Element Schemes For Two Classes Of Evolutional Differential Equations

This paper is composed of two parts. Firstly, We use a Crouzeix-Raviart type non-conforming trianglular element to approximate the hyperbolic type integro-differential equation, and a new mixed finite element scheme is established for this kind problem. The uniformity of the traditional Riese projection and the finite element interpolation is proved. Then, We get the same optimal error estimates as the conforming finite elements, At the same time, the H1-norm is derived,which can not be obtained for the usual mixed finite element schemes. Secondly, A linear anisotropic triangular element is applied to the generalized nerve conduction type equation. Under the new formulation, by use of the mean-value and derivative delivery technique and instead of the generalized Ritz projec-tion, We get the optimal error estimates in L2-norm. At last, The optimal error estimates of any order finite element method also is given for the generalized nerve conduction type equation.