Split Least-squares Mixed Finite Element Methods For Pseudo-parabolic Integro-differential Equations

This paper discusses split least-squares mixed finite element procedures for pseudo-parabolic integro-differential equations,and verifies the effectiveness of the methods through numerical experiments.By this method,the solution to the equation is stable,and we can select the finite element spaces more flexibly at the same time.By introducing an auxiliary variable to split the initial problem into lower order system,the method is optimal order approximation for the solution and its flux.Backward Euler and C-N formats on discrete-time items and a first-order linear interpolation on discrete space are used,thus error in the final result contains space discrete error and time discrete error.Because of the special nature of the equation,which orders one of the item to be zero,can be obtained by splitting least-squares mixed finite element method for pseudo-parabolic equations and by splitting least squares mixed finite element method for Non-Fickian flow.The main results of this paper are outlined as follows:In chapter one,the development process of pseudo-parabolic integro-differential equations,the background of the problem,and some basic konwledge used in the latter part of this paper are briefly introduced.In chapter two,split least squares mixed finite element method for pseudo-parabolic equations are discussed.It is proved that the scheme is essentially unconditionally stable and convergent.In chapter three,split least squares mixed finite element method for Non-Fickian flow are introduced.It is proven that the scheme is essentially unconditionally stable and convergent.In chapter four,split least-squares mixed finite element procedures for pseudo-parabolic integro-differential equations are disscussed,and the convergence of the numerical scheme is presented.The thoretical results are illustrated by numerical examples.