Adaptive hp-versions of boundary element methods for elastic contact problems
Adaptive hp-versions of boundary element methods for elastic contact problems
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DOI：
10.1007/s00466-006-0109-y
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发表时间：
2007-04-01
影响因子：
4.1
通讯作者：
Stephan, Ernst P.
中科院分区：
文献类型：
--
作者：
Maischak, Matthias;Stephan, Ernst P.
弹性接触问题的变分形式导致凸子集上的变分不等式。利用Poincare-Steklov算子，用边界元法求解这些变分不等式。该算子的离散化形式可用单层势算子、双层势算子和超奇异积分算子的稠密Galerkin矩阵的Schur补表示。由于凸子集离散化的困难，传统上只使用h-版本进行离散化。最近，在Maischak和Stephan（Appl Numer Math，2005）中，Signorini接触问题引入了p-和hp-版本。在本文中，我们证明了弹性接触问题边界元法的准一致hp版本的收敛性，并推导出自适应hp算法的后验误差估计和误差指标。我们提出了相应的数值实验。
The variational formulation of elastic contact problems leads to variational inequalities on convex subsets. These variational inequalities are solved with the boundary element method (BEM) by making use of the Poincare-Steklov operator. This operator can be represented in its discretized form by the Schur-complement of the dense Galerkin-matrices for the single layer potential operator, the double layer potential operator and the hypersingular integral operator. Due to the difficulties in discretizing the convex subsets involved, traditionally only the h-version is used for discretization. Recently, p- and hp-versions have been introduced for Signorini contact problems in Maischak and Stephan (Appl Numer Math, 2005) . In this paper we show convergence for the quasi-uniform hp-version of BEM for elastic contact problems, and derive a-posteriori error estimates together with error indicators for adaptive hp-algorithms. We present corresponding numerical experiments.