We introduce a new variational numerical method which does not require any background mesh to compute the scheme coefficients. Replacing the mesh by a point cloud endowed with connectivity, which we call a discretization network, and following the virtual element framework we derive a consistent, coercive and stable numerical scheme. We illustrate the good behavior of the method on several numerical examples.

中文翻译：

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网元方法原理

我们引入了一种新的变分数值方法，该方法不需要任何背景网格即可计算方案系数。用赋予连接性的点云替换网格，我们将其称为离散化网络，然后根据虚拟元素框架，得出一致，强制和稳定的数值方案。我们在几个数值示例上说明了该方法的良好行为。