AI 中文总结
该研究针对近似区域提出无需对齐法向的Neumann边界条件处理新方法，可处理网格聚合得到的区域，能证明虚拟单元离散任意阶的最优误差估计。
AI 中文摘要
在采用偏移边界类型处理弯曲几何的虚拟单元方法框架下，我们提出一种处理Neumann边界条件的新方法，该方法无需使物理法向与数值法向近似对齐，因此非常适合处理由底层精细结构化网格通过聚合得到的区域近似。针对该方法，我们给出了可证明虚拟单元离散任意阶最优误差估计的条件。
英文摘要
In the framework of the virtual element method with shifted boundary type treatment of curved geometries, we propose a novel approach to the treatment of Neumann boundary conditions that does not require the approximate aligning of the physical and numerical normal directions and is therefore well suited to handle domain approximations obtained by agglomeration from underlying fine structured grids. For such an approach we give conditions under which we are able to prove optimal error estimates for arbitrary orders of the virtual element discretization.
Comments27 pages, 6 figures
