论文标题
一种实用算法，可最大程度地减少FEM计算中的总体错误
A practical algorithm to minimize the overall error in FEM computations
论文作者
论文摘要
使用标准有限元方法（FEM）求解一般的偏微分方程，发现圆形误差与$ n^{β{\ rm rm r}} $成比例，$ n $具有自由度（DOFS）和$β__{\ rm rm rm rm r} $ a ceeff的$ n $。提出了一种使用一些廉价数值实验的方法来确定相称的系数和$β_ {\ rm rm} $在各种空间维度和FEM软件包中。使用上面获得的系数，在\ cite {liu386 balbalancing}中提出的策略预测了最高可实现的准确性$ e _ {\ rm min} $，并且针对特定问题的最佳dofs $ n _ {\ rm opt} $相关的最佳数量扩展到一般问题。此策略允许准确预测$ e _ {\ rm min} $，以解决一般问题，而CPU的时间用于获得具有最高精度的解决方案$ e _ {\ rm min} $通常减少60 \％-90 \％。
Using the standard finite element method (FEM) to solve general partial differential equations, the round-off error is found to be proportional to $N^{β_{\rm R}}$, with $N$ the number of degrees of freedom (DoFs) and $β_{\rm R}$ a coefficient. A method which uses a few cheap numerical experiments is proposed to determine the coefficient of proportionality and $β_{\rm R}$ in various space dimensions and FEM packages. Using the coefficients obtained above, the strategy put forward in \cite{liu386balancing} for predicting the highest achievable accuracy $E_{\rm min}$ and the associated optimal number of DoFs $N_{\rm opt}$ for specific problems is extended to general problems. This strategy allows predicting $E_{\rm min}$ accurately for general problems, with the CPU time for obtaining the solution with the highest accuracy $E_{\rm min}$ typically reduced by 60\%--90\%.
