We present a systematic description and comparison of the Finite Element Method (FEM) with the relatively new Virtual Element Method (VEM) for solving boundary value problems in linear elasticity, including primal and mixed formulations. The description highlights the common base and the essential difference between FEM and VEM: discretisation of the same primal (Galerkin) and mixed weak formulations and assembly of element-wise quantities, but different approaches to element shape functions. The mathematical formulations are complemented with detailed description of the computer implementation of all methods, including all versions of VEM, which will benefit readers willing to develop their own computational framework. Numerical solutions of several boundary value problems are also presented in order to discuss the weaker and stronger sides of the methods.

我们提供了有限元方法 (FEM) 与相对较新的虚拟元方法 (VEM) 的系统描述和比较，用于解决线性弹性中的边界值问题，包括原始公式和混合公式。描述强调了 FEM 和 VEM 之间的共同基础和本质区别：相同原始 (Galerkin) 和混合弱公式的离散化以及元素量的组装，但单元形状函数的不同方法。数学公式与所有方法的计算机实现的详细描述相辅相成，包括所有版本的 VEM，这将使愿意开发自己的计算框架的读者受益。