A Gårding Inequality Based Unified Approach to Various Classes of Semi-Coercive Variational Inequalities Applied to Non-Monotone Contact Problems with a Nested Max-Min Superpotential
Keywords:
Hemivariational inequality, pseudomonotonicity, semicoercivity, Gårding inequality, max-min superpotential, smoothing approximation, finite element discretization, non-monotone contact.Abstract
We present a unified existence and approximation theory for various classes of variational inequalities (VIs) in reflexive Banach spaces. The focus is on semi-coercive problems. Here we abandon projections, which are limited to a Hilbert space setting, instead we adopt semicoercivity of the elliptic linear operator in form of a Gårding inequality. Also we extend the smoothing procedure from [43] to provide smoothing approximations of nested max-min functions. Then we couple this regularization technique with the finite element method to solve numerically semi-coercive hemivariational inequalities (HVIs) involving a nested max-min superpotential
and apply our approximation theory for pseudomonotone VIs to these HVIs. As a model example we consider a unilateral semi-coercive contact problem with non-monotone friction on the contact boundary.
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