We study a priori error estimates of discontinuous Galerkin (DG) methods for solving a quasi-variational inequality, which models a frictional contact problem with normal compliance. In Xiao et al. (Numer Funct Anal Optim 39:1248–1264, 2018), several DG methods are applied to solve quasi-variational inequality, but no error analysis is given. In this paper, the unified numerical analysis of these DG methods is established, and they achieve optimal convergence order for linear elements. Two numerical examples are given, and the numerical convergence orders match well with the theoretical prediction.

中文翻译：

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拟变分不等式的不连续Galerkin方法的先验误差估计

我们研究了不连续Galerkin（DG）方法的先验误差误差估计，用于解决准变分不等式，该不等式模拟了具有正常柔量的摩擦接触问题。在Xiao等人中。（Numer Funct Anal Optim 39：1248–1264，2018），几种DG方法用于解决拟变分不等式，但未进行误差分析。在本文中，建立了这些DG方法的统一数值分析，并获得了线性元素的最优收敛阶。给出了两个数值例子，数值收敛阶次与理论预测吻合良好。