大长宽比单元有限元误差分析及高精度计算

针对大长宽比单元将传统的基于单元整体尺度的有限元误差估计扩展为基于单元不同方向尺度的误差估计;根据不同方向误差应该同量级的思想,得到了误差匹配准则.该准则可以作为网格划分的判据.根据这一匹配准则,提出了一种提高计算精度的方法--单向高次插值法.数值实验表明该误差估计是正确的,误差匹配准则作为网格划分的判据是有效的,采用合理的有限元插值逼近能够有效地减小计算误差,提高计算的精度和效率.

Error analysis of high-aspect-ratio finite elements for 2-D boundary layer simulations

A new error analysis in finite element method, which is based on the element size in spatial directions respectively, was proposed. This analysis is different from the ordinary error analysis method, which is based on the overall size of elements. An error matching principle can be derived from the analysis presented here. The principle can be used in generating optimal grids and in analyzing the error of the calculation. A high precision finite element scheme was discussed upon the error matching principle, that uses the high order interpolation in the desired direction. The new error analysis method and the error matching principle were verified by the numerical tests. The results show that the proper grid sizes and right order of interpolation can minimize the error and improve the computational efficiency.