论文标题
关于通过不同数值方法获得的截断和近似误差的关系
On the relation of truncation and approximation errors for the set of solutions obtained by different numerical methods
论文作者
论文摘要
根据二维稳定稳定无粘性可压缩流的情况，计算并分析了通过方法计算出的基于不同结构算法计算的数值解的截断和近似误差。使用特殊的后处理器计算截断误差，而近似误差是通过比较数值解决方案和分析方法获得的。数值溶液的误差独立性的程度可以通过Pearson相关系数估算，该系数可以通过误差之间的角度表达几何表达。由于这个原因，计算近似误差之间的角度，并与截断误差之间的相应角度相关。发现近似误差之间的角度远非零，可以对误差规范进行后验估计。对这些解决方案之间距离的分析为估计误差提供了另一种方法。提供了通过这两个程序获得的误差规范的比较，以证明其效率指数的可接受值。提出了超音速流的近似误差规范估计的结果，包含冲击波。测量浓度现象和算法随机性为这些结果提供了一些见解。
The truncation and approximation errors for the set of numerical solutions computed by methods based on the algorithms of different structure are calculated and analyzed for the case of the two-dimensional steady inviscid compressible flow. The truncation errors are calculated using a special postprocessor, while the approximation errors are obtained by the comparison of the numerical solution and the analytic one. The extent of the independence of errors for the numerical solutions may be estimated via the Pearson correlation coefficient that may be geometrically expressed by the angle between errors. Due to this reason, the angles between the approximation errors are computed and related with the corresponding angles between the truncation errors. The angles between the approximation errors are found to be far from zero that enables a posteriori estimation of the error norm. The analysis of the distances between these solutions provides another approach to the estimation of the error. The comparison of the error norms, obtained by these two procedures, is provided that demonstrates the acceptable values of their effectivity indices. The results of the approximation error norm estimation for the supersonic flows, containing shock waves, are presented. The measure concentration phenomenon and the algorithmic randomness give some insights into these results.
