A Class of Variational-Hemivariational Inequalities with Applications to Frictional Contact Problems

Weimin Han (1) , Stanisław Migórski (2) , Mircea Sofonea (3)

1 Department of Mathematics, University of Iowa
2 Institute of Computer Science [Krakow]
3 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations

A class of variational-hemivariational inequalities is studied in this paper. An inequality in the class involves two nonlinear operators and two nondfferentiable functionals, of which at least one is convex. An existence and uniqueness result is proved for a solution of the inequality. Continuous dependence of the solution on the data is shown. Convergence is established rigorously for finite element solutions of the inequality. An error estimate is derived which is of optimal order for the linear finite element method under appropriate solution regularity assumptions. Finally, the results are applied to a variational-hemivariational inequality arising in the study of some frictional contact problems.

Mots clés: variational-hemivariational inequality; Clarke subdifferential; existence and uniqueness; continuous dependence; finite element solution; convergence; error estimates; frictional contact

Domaines: Mathématiques [math]

Weimin Han, Stanisław Migórski, Mircea Sofonea. A Class of Variational-Hemivariational Inequalities with Applications to Frictional Contact Problems. SIAM Journal on Mathematical Analysis, 2014, 46 (6), pp.3891-3912. ⟨10.1137/140963248⟩. ⟨hal-01142712⟩