论文标题
对各向异性网格的插值误差估计的一般理论
General theory of interpolation error estimates on anisotropic meshes
论文作者
论文摘要
我们提出了一种估计两个维度和三个维度平滑功能的插值误差的一般理论。在我们的理论中，插值的误差是根据单纯的直径和几何参数结合的。在二维情况下，我们的几何参数等效于三角形的craldius。在三维情况下，我们的几何参数也代表四面体的平坦度。通过引入几何参数，新获得的错误估计可以应用于违反最大角度条件的情况。
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.
