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On convergence of numerical methods for variational-hemivariational inequalities under minimal solution regularity. (English) Zbl 1412.49027

Summary: Hemivariational inequalities have been successfully employed for mathematical and numerical studies of application problems involving nonsmooth, nonmonotone and multivalued relations. In recent years, error estimates have been derived for numerical solutions of hemivariational inequalities under additional solution regularity assumptions. Since the solution regularity properties have not been rigorously proved for hemivariational inequalities, it is important to explore the convergence of numerical solutions of hemivariational inequalities without assuming additional solution regularity. In this paper, we present a general convergence result enhancing existing results in the literature.

MSC:

49J40 Variational inequalities
49M25 Discrete approximations in optimal control
49N60 Regularity of solutions in optimal control
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