We develop a lowest-order nonconforming virtual element method for planar linear elasticity in the pure traction formulation, which can be viewed as an extension of the idea in Falk (1991) to the virtual element method, with the family of polygonal meshes satisfying a very general geometric assumption. A discrete Korn's inequality is established. And the method is shown to be uniformly convergent for the nearly incompressible case with an optimal convergence rate.

翻译：我们为纯牵引配方中的平面线性弹性开发了一种最低顺序不兼容的虚拟元素方法,这可被视为Falk(1991年)中的概念向虚拟元素方法的延伸,而多边形网关组符合非常一般的几何假设。确立了离散式科恩的不平等。对于几乎无法压缩的病例,该方法与最佳趋同率一致。