We introduce a nonconforming virtual element method for the Poisson equation on domains with curved boundary and internal interfaces. We prove arbitrary order optimal convergence in the energy and $L^2$ norms, and validate the theoretical results with numerical experiments. Compared to existing nodal virtual elements on curved domains, the proposed scheme has the advantage that it can be designed in any dimension.
翻译:本文针对具有弯边和内部界面的Poisson方程引入了一种非切线虚拟单元方法。我们证明在能量和$L^2$范数下都能够获得任意阶最优收敛性能,并利用数值实验验证了理论结果。与现有的在弯曲区域中的节点虚拟单元相比,所提出的方案具有在任意维度中进行设计的优势。