In this article, a recovery by compatibility in patches (RCP)‐based a posteriori error estimator is proposed for the virtual element method (VEM), and it is utilized to drive adaptive mesh refinement processes in two‐dimensional elasticity problems. In RCP, recovered stresses are obtained by minimizing the complementary energy of patches of elements over a set of assumed equilibrated stress modes. To this aim, the explicit knowledge of displacements is only needed along the patch boundaries and no knowledge of superconvergent points is required, so making the RCP naturally suitable for the VEM. The a posteriori error estimation is conducted by comparing the stress field of a standard displacement‐based VEM solution and the stress field obtained through RCP. The procedure is simple, and it does not require ad hoc modifications for small patches. The capability of this RCP‐based error estimator to drive adaptive mesh refinements is successfully demonstrated through various numerical examples.

中文翻译：

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基于补丁兼容性恢复的虚拟单元法误差估计和网格自适应

本文针对虚拟元素方法（VEM）提出了一种基于补丁的兼容性恢复（RCP）的后验误差估计器，并将其用于驱动二维弹性问题中的自适应网格细化过程。在RCP中，通过在一组假定的平衡应力模式上最小化元素补丁的互补能量来获得恢复的应力。为此，仅需要沿面片边界明确了解位移，而无需了解超会聚点，因此使RCP自然适用于VEM。在后验通过将基于位移的标准VEM解决方案的应力场与通过RCP获得的应力场进行比较，可以进行误差估计。该过程很简单，不需要针对小补丁进行临时修改。通过各种数值示例成功地证明了这种基于RCP的误差估计器驱动自适应网格细化的能力。