We propose a general theory of estimating interpolation error for smooth functions in two and three dimensions. In our theory, the error of interpolation is bound in terms of the diameter of a simplex and a geometric parameter. In the two-dimensional case, our geometric parameter is equivalent to the circumradius of a triangle. In the three-dimensional case, our geometric parameter also represents the flatness of a tetrahedron. Through the introduction of the geometric parameter, the error estimates newly obtained can be applied to cases that violate the maximum-angle condition.

中文翻译：

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各向异性网格插值误差估计的一般理论

我们提出了一种估计二维和三维平滑函数插值误差的一般理论。在我们的理论中，插值误差受限于单纯形的直径和几何参数。在二维情况下，我们的几何参数等价于三角形的外接圆半径。在三维情况下，我们的几何参数也表示四面体的平面度。通过引入几何参数，新得到的误差估计可以应用于违反最大角度条件的情况。