Abstract

A grid analog of the formula of integration by parts is constructed and studied for a two-dimensional case in which one of the grid functions is defined at nodes, and the second function is defined at the midpoints of the sides of cells of a simplicial grid in the Cartesian and cylindrical systems of coordinates. Grid analogs of such first-order differential operators as the gradient, divergence, and curl operators, can be naturally defined using this formula.

中文翻译：

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差值微分算子的值在三角形网格的边的中点

摘要

针对二维情况构造并研究了按部分积分的公式的网格模拟，其中在一个节点上定义了一个网格函数，在一个简单网格的单元格的边的中点定义了第二个函数在直角坐标系和圆柱坐标系中。可以使用此公式自然定义诸如梯度，散度和卷曲运算符等一阶微分运算符的网格模拟。