接触力学中双历史相关变分不等式的数值分析

Fixed Point Theory and Applications Pub Date : 2021-12-13 DOI:10.1186/s13663-021-00710-7

Xu, Wei, Wang, Cheng, He, Mingyan, Chen, Wenbin, Han, Weimin, Huang, Ziping

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引用次数: 3

摘要

本文对接触力学中的双历史相关变分不等式进行了数值分析。介绍了一种完全离散的变分不等式逼近方法，其中双历史相关算子用重复左端点规则逼近，空间变量用线性元法逼近。在适当的求解规则下，给出了最优阶误差估计，并通过数值算例说明了该方法的收敛阶数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Numerical analysis of doubly-history dependent variational inequalities in contact mechanics

This paper is devoted to numerical analysis of doubly-history dependent variational inequalities in contact mechanics. A fully discrete method is introduced for the variational inequalities, in which the doubly-history dependent operator is approximated by repeated left endpoint rule and the spatial variable is approximated by the linear element method. An optimal order error estimate is derived under appropriate solution regularities, and numerical examples illustrate the convergence orders of the method.

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Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.