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arXiv 1208.6478math.NAcs.NAmath-phmath.MP
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弹性单边多体接触问题的惩罚Robin-Robin区域分解方法的收敛性

Convergence of penalty Robin-Robin domain decomposition methods for unilateral multibody contact problems of elasticity

Ivan Franko National University of Lviv（伊万·弗兰科大学）；Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine（乌克兰国家科学院皮德斯特雷哈赫应用力学与数学问题研究所）

Ivan I. Dyyak, Ihor I. Prokopyshyn, Ivan A. Prokopyshyn

备注：
33 pages, 8 figures; introduction was improved, more references were added, some minor changes were made
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AI总结：

本文针对弹性单边多体接触问题，提出了基于惩罚法的Robin-Robin区域分解方法，并证明了其收敛性定理，同时通过有限元近似验证了数值效率。

摘要：

本文致力于研究我们提出的用于求解弹性单边多体接触问题的惩罚Robin-Robin区域分解方法（DDMs）。这些DDMs基于变分不等式的惩罚法以及非线性变分方程的某些稳态和非稳态迭代方法。本文的主要结果是给出了所提DDMs的数学证明，并证明了其收敛性定理。我们还利用有限元近似研究了这些方法的数值效率。

英文摘要：

The paper is devoted to the penalty Robin-Robin domain decomposition methods (DDMs), proposed by us for the solution of unilateral multibody contact problems of elasticity. These DDMs are based on the penalty method for variational inequalities and some stationary and nonstationary iterative methods for nonlinear variational equations. The main result of the paper is that we give the mathematical justification of proposed DDMs and prove theorems on their convergence. We also investigate the numerical efficiency of these methods using the finite element approximations.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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