The Error Estimation in Finite Element Method for the Linear Elasticity Problems

摘要

In the dissertation, we study the error estimation in finite element method for linear elasticity. In Chapter 1, we briefly introduce the linear elasticity problems and the formal definitions of operators and spaces. In Chapter 2, the locking free discontinuous Galerkin (DG) finite element method for interface problems is introduced and optimal error estimate is established. To this end, we introduce a nonstandard variational formulation with parameters to penalize jump terms. In Chapter 3, we develop the least-squares finite element method by strongly imposing the symmetry condition for the stress. Then, we establish a priori error estimate and analyze momentum balance error. In Chapter 4, we develop and analyze two least-square methods for linear elasticity and Stokes equations. We also establish optimal error estimates in the energy norm and L2 norm.