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 work, we consider adaptive mesh refinement for a monolithic phase‐field description
for fractures in brittle materials. Our approach is based on an a posteriori error estimator for …

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 …

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 …

We consider the numerical solution of a variational inequality arising in the study of an
incompressible Stokes flow with a nonlinear slip boundary condition of frictional type. We …

We present a posteriori error analysis in the supremum norm for the symmetric interior
penalty discontinuous Galerkin method for the elliptic obstacle problem. We construct …

In this article, we study a posteriori error analysis of quadratic finite element method in the
maximum norm for the elliptic obstacle problem. We discuss the reliability and the efficiency …

We perform a posteriori error analysis in the supremum norm for the quadratic discontinuous
Galerkin method for the elliptic obstacle problem. We define two discrete sets (motivated by …

In this article, we develop a posteriori error analysis of a non-conforming finite element
method in the supremum norm for the elliptic obstacle problem. In the analysis, the proper …