On Semicoercive Variational-Hemivariational Inequalities—Existence, Approximation, and Regularization
On Semicoercive Variational-Hemivariational Inequalities—Existence, Approximation, and Regularization
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DOI：
10.1007/s10013-018-0282-2
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发表时间：
2018-03
影响因子：
0.8
通讯作者：
O. Chadli;J. Gwinner;N. Ovcharova
中科院分区：
文献类型：
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作者：
O. Chadli;J. Gwinner;N. Ovcharova
在本文中，我们关注半强制变分-半变分不等式，其中包括自反 Banach 空间中的非线性半强制单调变分不等式 (VI) 和伪单调 VI，以及函数空间中的半变分不等式 (HVI)。我们提出存在性、近似性和正则化结果。我们对生存结果的态度是基于经济衰退的论点。我们采用不可微优化的正则化技术来平滑半变分项中的跳跃。我们通过 Mosco 收敛来处理非相容有限元近似。作为一个例子，我们考虑具有非单调边界条件的半强制单边边值问题，该问题模拟非单调摩擦定律下非线性弹性体的单边接触问题。
In this paper, we are concerned with semicoercive variational-hemivariational inequalities that encompass nonlinear semicoercive monotone variational inequalities (VIs) and pseudomonotone VIs in reflexive Banach spaces and hemivariational inequalities (HVIs) in function spaces. We present existence, approximation, and regularization results. Our approach to our existence result is based on recession arguments. We employ regularization techniques of nondifferentiable optimization to smooth the jumps in the hemivariational term. We treat nonconforming finite element approximation via Mosco convergence. As an example, we consider a semicoercive unilateral boundary value problem with nonmonotone boundary conditions that models a unilateral contact problem for a nonlinear elastic body under a nonmonotone friction law.