本项目旨在研究三维弹性问题自适应弱Galerkin有限元方法。通过对大量现有文献的调研，发现弱Galerkin有限元方法既继承了传统有限元方法的良好特点，又具有间断有限元方法的很多优点，因而采用自适应弱Galerkin有限元方法来求解三维弹性问题应当是非常有效的。为了实现本项目的研究目标，我们制定了详细的研究方案，拟从以下四个方面进行探讨:(1)针对协调和非协调的网格剖分，分别设计误差指示子及自适应弱Galerkin有限元算法;(2)研究所设计的算法的收敛性;(3)通过引入震荡项和非线性逼近类，研究所设计的算法的最优复杂性;(4)设计程序，通过数值实验测试理论结果的正确性。开展对本项目的研究将在偏微分方程相关理论中具有重要的创新意义，同时项目成果会对弹性力学领域的研究起到积极作用。

The goal of this project is to study adaptive weak Galerkin finite element method for three dimensional linear elasticity problems. By comparison of a deal of literatures, we conclude that the weak Galerkin finite element method has a lots of good characteristics of the traditional finite element method and many advantages of the discontinuous finite element method, which make this method be considered as a powerful and effective way to solve three dimensional linear elasticity problems. In order to achieve the goal of this project, we have elaborated a detailed research program, and will carry it out in the following respects: (1) Designing two kinds of error estimators and adaptive weak Galerkin finite element algorithms based on conforming mesh or nonconforming mesh.(2)Studying the convergence of the corresponding algorithms. (3) Studying the optimal complexity of the algorithms by defining the oscillation and the nonlinear approximation class. (4) Designing algorithms and verifying these theoretical results through sorts of numerical experiments. The successful accomplishment of this project will yield a significant innovation to PDE theory, and also can contribute to research in fields of elasticity.