Contact phenomena arise in a variety of industrial process and engineering applications.
For this reason, contact mechanics has attracted substantial attention from research …

In this paper we will present a review of recent advances in the application of the augmented
Lagrange multiplier method as a general approach for generating multiplier-free stabilised …

In this paper, we investigate a nonlinear and nonsmooth dynamics system (NNDS, for short)
involving two multi-valued maps which are a convex subdifferential operator and a …

We present two primal methods to weakly discretize (linear) Dirichlet and (nonlinear)
Signorini boundary conditions in elliptic model problems. Both methods support polyhedral …

In this work, several discontinuous Galerkin (DG) methods are introduced and analyzed to
solve a variational inequality from the stationary Navier–Stokes equations with a nonlinear …

We study virtual element methods (VEMs) for solving the obstacle problem, which is a
representative elliptic variational inequality of the first kind. VEMs can be regarded as a …

In this article, we derive an a posteriori error estimator for various discontinuous Galerkin
(DG) methods that are proposed in (Wang, Han and Cheng, SIAM J. Numer. Anal., 48: 708 …

This work aims at studying the virtual element method (VEM) to solve a simplified friction
problem, which is a typical elliptic variational inequality of the second kind. An optimal error …

This paper is devoted to virtual element methods for solving elliptic variational inequalities
(EVIs) of the second kind. First, a general framework is provided for the numerical solution of …

A weak-Galerkin finite element method is used to determine approximate solutions of an
elliptic variational inequality. Three sets of basis functions are employed: the first has …