Finite Element Method For Two Types Of Differential Equations

The main aim of this paper is to study the method of a two order nonconforming finite element to viscoelasticity type equations and the finite element method to the eigenvalues for crosswise vibration equation of a bean with continuous load.Chapter three in detail researchs the approximation to viscoelasticity type equations of a nonconforming finite element with 5NP degrees of freedom.It is also proved that the order of error is O(h2) without employing the postprocessing techniqueIn chapter four the paper is to study the finite element method to the eigenvalues for crosswise vibration equation of a bean with continuous load which can be related to a differential-integral equation. According to certain theories of completely continuous opera-tor, the existence of the eigenvalues is given at first, and then the error estimates of the finite element approximate solution and weak solution of differential-integral equation arc obtained as well, which the order of error is optimal.