A priori error estimates of discontinuous Galerkin methods for a quasi-variational inequality

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.