We present the construction and application of a first order stabilization-free virtual element method to problems in plane elasticity. Well-posedness and error estimates of the discrete problem are established. The method is assessed on a series of well-known benchmark problems from linear elasticity and numerical results are presented that affirm the optimal convergence rate of the virtual element method in the $L^2$ norm and the energy seminorm.

翻译：本文介绍了一阶无稳定化虚拟单元法在平面弹性问题中的构造与应用。建立了离散问题的适定性和误差估计。通过一系列线性弹性经典基准问题进行方法评估，数值结果验证了虚拟单元法在$L^2$范数和能量半范数下的最优收敛速度。