A penalty method for history-dependent variational-hemivariational inequalities
A penalty method for history-dependent variational-hemivariational inequalities
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DOI：
10.1016/j.camwa.2017.12.018
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
M. Sofonea;S. Migórski;W. Han
中科院分区：
文献类型：
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作者：
M. Sofonea;S. Migórski;W. Han
当罚参数趋于零时，罚方法通过一系列无约束的变分或半变分不等式逼近约束变分或半变分不等式。这些方法不仅适用于约束问题的数值求解，而且也是证明约束问题解的存在性的有效工具。本文对一类具有历史依赖算子的变分-半变分不等式的罚方法进行了理论分析。证明了惩罚问题的唯一可解性，以及当惩罚参数趋于零时，其解收敛于原历史依赖的变分半变分不等式的解.所得收敛性结果推广了已有的几个罚方法的收敛性结果。最后，将理论结果应用于描述粘弹性杆和反应基础之间的准静态接触的数学模型中的历史相关的变分半变分不等式的例子。
Penalty methods approximate a constrained variational or hemivariational inequality problem through a sequence of unconstrained ones as the penalty parameter approaches zero. The methods are useful in the numerical solution of constrained problems, and they are also useful as a tool in proving solution existence of constrained problems. This paper is devoted to a theoretical analysis of penalty methods for a general class of variational–hemivariational inequalities with history-dependent operators. Unique solvability of penalized problems is shown, as well as the convergence of their solutions to the solution of the original history-dependent variational–hemivariational inequality as the penalty parameter tends to zero. The convergence result proved here generalizes several existing convergence results of penalty methods. Finally, the theoretical results are applied to examples of history-dependent variational–hemivariational inequalities in mathematical models describing the quasistatic contact between a viscoelastic rod and a reactive foundation.