On the circumradius condition for piecewise linear triangular elements
On the circumradius condition for piecewise linear triangular elements
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关于分段线性三角形单元的外接圆半径条件
DOI：
10.1007/s13160-014-0161-5
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发表时间：
2015
影响因子：
0.9
通讯作者：
T. Tsuchiya
中科院分区：
文献类型：
--
作者：
K. Kobayashi;T. Tsuchiya
讨论了三角形单元上线性插值的误差分析。我们认为，对于有限元法的收敛性，特别是对于线性拉格朗日有限元，外切半径条件比著名的最大角条件更为重要。数值实验表明，这种条件是最好的。我们还指出，外切半径条件与表面积的定义密切相关。
We discuss the error analysis of linear interpolation on triangular elements. We claim that the circumradius condition is more essential than the well-known maximum angle condition for convergence of the finite element method, especially for the linear Lagrange finite element. Numerical experiments show that this condition is the best possible. We also point out that the circumradius condition is closely related to the definition of surface area.