This paper is devoted to the numerical solution of a fourth-order elliptic variational inequality of the first kind by the virtual element method (VEM). The variational inequality models an obstacle problem for the Kirchhoff-Love plate. Both conforming and fully nonconforming VEMs are studied to solve the fourth-order elliptic variational inequality. Optimal order error estimates are derived in the discrete energy norm, under certain solution regularity assumptions. The primal-dual active algorithm is applied to solve the discrete problems. Numerical examples are reported to show the performance of the numerical methods and to illustrate the convergence orders of the numerical solutions.

本文致力于用虚元法（VEM）数值解第一类四阶椭圆变分不等式。变分不等式模拟了 Kirchhoff-Love 板块的障碍问题。研究符合和完全不符合 VEM 以解决四阶椭圆变分不等式。在某些解正则假设下，在离散能量范数中导出最优阶误差估计。原始对偶主动算法用于解决离散问题。报告了数值例子以显示数值方法的性能并说明数值解的收敛阶次。