h-自适应边界元方法的插值残差计算及误差估计

The Calculation of Interpolation Residue and Error Estimation in h-adaptive Boundary Element Method

本文提出了一种用于估计h-自适应边界元过程解误差的新方法。这种方法基于h-自适应边界元过程生成的离散网格,通过计算近似解的插值残差,以此作为误差估计的依据。此外,这种误差分析方法方法易于程序化,可以很方便地接入现有h-自适应边界元计算机程序(简单细分或分层细分),而对原程序不作大的改动。通过对二个经典的弹性静力学问题的分析表明:本文的方法能较好地估计边界元解的误差,并使h-自适应边界元程序的分析更加有效可靠。

In this paper, a new method of error estimation was suggested on h-ddaptive boundary element method. Based on the discrete meshes that are generated for the process of h-adaptive refinement, the solution error was estimated by the interpolation residue. In addition, this method is easy to programming, and with less modification to be introduced into the current codes of h- adaptive boundary elements (simple refinement or hierarchical refinement) . Its validity and effectiveness have been confirmed by two classic elastostatics problems.