This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal convergence in the energy and $L^2$ norms, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the method is shown to be comparable with the theoretical analysis.

翻译：本文针对具有曲边边界和曲边内部界面的一般变系数二阶椭圆问题，提出了一种非协调虚拟元方法。我们证明了该方法在能量范数和$L^2$范数下具有任意阶最优收敛性，并通过在一系列多边形网格上的数值实验验证了该结论。数值实验表明，该方法提供的数值逼近精度与理论分析结果一致。