An adaptive finite element discretisation¶for a simplified Signorini problem
An adaptive finite element discretisation¶for a simplified Signorini problem
复制标题
简化 Signorini 问题的自适应有限元离散化¶
DOI：
10.1007/s100920070008
复制
发表时间：
2000
期刊：
影响因子：
1.7
通讯作者：
F. Suttmeier
中科院分区：
文献类型：
--
作者：
H. Blum;F. Suttmeier
摘要：研究了基于后验误差控制的自适应网格设计，用于Signorini型变分问题的有限元离散化。例如，在（[2,10,20]）中开发的导出基于残差的误差估计器的技术被扩展到采用对偶性论证的适当适应的变分不等式[17]。通过使用这种变分参数加权，可以针对接触问题的模型情况导出用于控制误差的任意函数的后验估计。所有论证都基于希尔伯特空间方法，并且可以推广到更一般的线性弹性情况。数值示例表明，这种方法可以提供设计经济网格的有效策略，并确定在实践中有用的误差范围。
Abstract:Adaptive mesh design based on a posteriori error control is studied for finite element discretisations for variational problems of Signorini type. The techniques to derive residual based error estimators developed, e.g., in ([2, 10, 20]) are extended to variational inequalities employing a suitable adaptation of the duality argument [17]. By use of this variational argument weighted a posteriori estimates for controlling arbitrary functionals of the error are derived here for model situations for contact problems. All arguments are based on Hilbert space methods and can be carried over to the more general situation of linear elasticity. Numerical examples demonstrate that this approach leads to effective strategies for designing economical meshes and to bounds for the error which are useful in practice.