On Semicoercive Variational-Hemivariational Inequalities—Existence, Approximation, and Regularization

On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology

“…Remark 3.3. As mentioned in the introduction, previous analyses of finite element approximations of semicoercive variational inequalities either only consider the error in a seminorm [31] or use indirect arguments to prove the convergence of the approximate solution in the complete norm [42,25,40,2,8]. In these cases, arguments by contradiction involving a sequence of triangulations are used.…”

On variational-hemivariational inequalities with nonconvex constraints

“…We refer to the book [5] where the existence, uniqueness, and convergence results for various class of variational-hemivariational inequalities were studied, as well as the applications of these inequalities in the study of mathematical models which describe the contact between a deformable body and a foundation. Recently, semicoercive variational-hemivariational inequalities were studied via regularization techniques, and used to model unilateral contact problems with nonmonotone boundary conditions as well as the delamination of composite structures with a contaminated interface layer; see, e.g., [6,7] and the references therein.…”

Existence of Solutions for a Class of Noncoercive Variational–Hemivariational Inequalities Arising in Contact Problems

“…The literature on hemivariational inequalities has been significantly enlarged in the last forty years, mainly because of their extensive applications, see [8,[13][14][15][16][23][24][25][26]29,34,38] for analysis of various classes of such inequalities. Recent results in the study of hemivariational inequalities can be found in [9,21,22,37]. There, various existence results have been proved, by using arguments of convexity, monotonicity, lower semicontinuity, fixed point and so on.…”