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On the p-version approximation in the boundary element method for a variational inequality of the second kind modelling unilateral contact and given friction

机译：边界元法中第二种建模单边接触和给定摩擦的变分不等式的p版本近似

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摘要

In this paper we complement recent work of Maischak and Stephan on adaptive hp-versions of the BEM for unilateral Signorini problems, respectively on FEM-BEM coupling in its h-version for a nonlinear transmission problem modelling Coulomb friction contact. Here we focus on the boundary element method in its p-version to treat a scalar variational inequality of the second kind that models unilateral contact and Coulomb friction in elasticity together. This leads to a nonconforming discretization scheme. In contrast to the work cited above and to a related paper of Guediri on a boundary variational inequality of the second kind modelling friction we take the quadrature error of the friction functional into account of the error analysis. At first without any regularity assumptions, we prove convergence of the BEM Galerkin approximation in the energy norm. Then under mild regularity assumptions, we establish an a priori error estimate that is based on a novel Cea-Falk lemma for abstract variational inequalities of the second kind.
机译：在本文中，我们对Maischak和Stephan在单边Signorini问题的BEM自适应hp版本上的最新工作进行了补充，分别在HEM版本的FEM-BEM耦合中建模了库仑摩擦接触的非线性传递问题。在这里，我们将重点放在边界元素方法的p版本中，以处理第二种标量变化不等式，该不等式将单侧接触和库仑摩擦共同建模。这导致不一致的离散化方案。与上面引用的工作以及Guediri的有关第二类建模摩擦的边界变分不等式的论文相反，我们将摩擦函数的正交误差考虑在内。首先，没有任何规则性假设，我们证明了BEM Galerkin逼近在能量范数中的收敛性。然后在轻度规律性假设下，我们建立了一个基于新的Cea-Falk引理的第二类抽象变分不等式的先验误差估计。

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