A priori error estimates for hp penalty BEM for contact problems in elasticity
A priori error estimates for hp penalty BEM for contact problems in elasticity
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DOI：
10.1016/j.cma.2006.10.044
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发表时间：
2007-08
影响因子：
7.2
通讯作者：
A. Chernov;M. Maischak;E. Stephan
中科院分区：
文献类型：
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作者：
A. Chernov;M. Maischak;E. Stephan
本文的目的是获得一个先验的误差估计的HP-版本的罚伽辽金边界元法应用于无摩擦接触问题的弹性。误差分析分为两部分。首先考虑变分不等式（或拉格朗日乘子）公式在罚问题下的近似误差。在额外的正则性假设下，我们得到了关于惩罚参数的线性收敛速度。然后考虑了罚问题的解与其Galerkin逼近之间的离散误差。我们证明了两种类型的最佳逼近性质，这是类似于Cea的引理，但估计依赖于惩罚参数。最后，我们得到了变分不等式的精确解u与罚问题的边界元Galerkin解之间的误差的先验估计。对于u∈H <$3/2（ΓC <$ΓN），当罚参数ε=C <$（h/p）1-n ∈（0;1）且C <$>0时，我们得到了收敛速度O（（h/p）1-n）.
The purpose of the paper is to obtain a priori error estimates for the hp-version of penalty Galerkin BEM applied to frictionless contact problems in elasticity. The error analysis is divided into two parts. At first we consider the error caused by the approximation of the variational inequality (or Lagrange multiplier) formulation with the penalty problem. Under additional regularity assumptions we derive a linear convergence rate with respect to the penalty parameter. Then the discretization error between the solution of the penalty problem and its Galerkin approximation is considered. We show two types of the best approximation property which is similar to the Cea’s lemma, but the estimate depends on the penalty parameter. Finally, we derive an a priori estimate for the error between the exact solution u of the variational inequality and the boundary element Galerkin solution of the penalty problem. For u∈H∼3/2(ΓC∪ΓN) we obtain the convergence rate O((h/p)1-ϵ) when choosing the penalty parameter ε=C∼(h/p)1-ϵfor arbitrary fixed ϵ∈(0;1) and C∼>0.