The Low-order R-T Element Method For Linear Elasticity Problem

This paper studies the numerical solution of the Dirichlet boundary value problem of linear elasticity problem using low-order mixed element method.The hybrid finite element method for linear elasticity problem is the displacement and stress are both included in the variational form,the mixed element approximation of displacement space and stress space are obtained in a discrete scheme,and the approximate values of displacement and stress are obtained by solving the linear equations.Firstly,we select the 0-order rectangular R-T element as the trial space to approximate the stress space;then select the piecewise constant to approximate the displacement space.Since the stress and displacement involved in linear elasticity are tensors,tensor analysis is introduced.And then after exporting the discrete format of the original problem,the existence and uniqueness of the solution of the discrete problem are proved by using the discrete B-B condition,and the error estimation is carried out.Because the original problem's stress tensor has symmetry,but the rectangular R-T element format is not necessarily symmetrical after approximation,so it is corrected by post-processing technology.Finally,some numerical experiments are carried out,and the numerical solutions obtained through inspection are smooth and consistent with the theoretical analysis.