论文标题
基于多边形像素的镶嵌的虚拟元素方法
The virtual element method on polygonal pixel-based tessellations
论文作者
论文摘要
我们分析和验证与[1,2]中类似的边界校正结合的虚拟元素方法，以解决具有多边形域近似弯曲边界的二维域上的问题。我们专注于从均匀结构的网格中获得的近似域的近似域的结合，例如当从图像发出域时自然出现的元素。我们在理论上和数字上都显示了诉诸于多边形元素的诉讼允许满足任何多项式顺序所需的假设。这使我们能够充分利用高阶方法的潜力。作用在分解边缘的新型静态冷凝策略来确保效率。
We analyze and validate the virtual element method combined with a boundary correction similar to the one in [1,2], to solve problems on two dimensional domains with curved boundaries approximated by polygonal domains. We focus on the case of approximating domains obtained as the union of squared elements out of a uniform structured mesh, such as the one that naturally arises when the domain is issued from an image. We show, both theoretically and numerically, that resorting to polygonal elements allows the assumptions required for stability to be satisfied for any polynomial order. This allows us to fully exploit the potential of higher order methods. Efficiency is ensured by a novel static condensation strategy acting on the edges of the decomposition.
