Discontinuous Galerkin methods for solving the Signorini problem

A posteriori error estimates of discontinuous Galerkin methods for the Signorini problem

“…For well-known DG methods, we verify (4.3). To this end, we recall from [3,47] that r 0 and r e denote global and local lifting operators, respectively. Recall that the bilinear form a h (., .)…”

“…The Signorini problem is a variational inequality of the first kind that arises from the study of frictionless contact problems [28]. Recently in [47], several DG methods have been proposed and their a priori error analysis has been derived for the Signorini problem. Independently in [21], a local discontinuous Galerkin (LDG) method has been proposed and analyzed for a simplified Signorini problem.…”

Discontinuous Galerkin Methods for an Elliptic Variational Inequality of Fourth-Order

“…In [21], numerous DG methods were extended for solving elliptic variational inequalities of second-order, and a priori error estimates were established, which are of optimal order for linear elements. DG methods for the Signorini problem and a quasistatic contact problem were also studied in [22,23], respectively. In this chapter, we study DG methods to solve an elliptic variational inequality of fourth-order for the Kirchhoff plates.…”

Rothe method for parabolic variational–hemivariational inequalities

“…For the recent results on numerical methods for static variational inequalities see for example [25], for hemivariational ones see [2,10] and for variational-hemivariational ones see [3,9,13]. Results for evolution variational inequalities are presented in [12,26], while for hemivariational ones in [13,14,27].…”