Numerical Methods For Two Kinds Of Boundary Value Problems

In this paper,numerical methods for the eigenvalue problem of plate bending and the second-order elliptic periodic boundary value problem are studied.For the first problem,a mixed variational form is obtained by introducing an auxiliary variable.Then,a nonconforming finite element discrete scheme is established using space of Crouzeix-Raviart element.Next,its original problem is analyzed,and the convergence of the related operator of the eigenvalue problem is obtained.Finally,numerical examples are given to show that the numerical method presented in this paper has certain effect.For the second problem,one-dimensional and two-dimensional problems are studied by Fourier-Petrov-Galerkin method.First,piecewise polynomial space is selected as the test space,which is different with solution space.Then,the discrete scheme of the original problem is obtained.Next,the existence and uniqueness of the solution of the discrete problem are proved by using Babuska theorem,and the error estimation is carried out.Finally,three numerical experiments are given,and numerical solutions are obtained,which are smooth and consistent with theoretical analysis.