Quadratic finite element approximation of the Signorini problem
Quadratic finite element approximation of the Signorini problem
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DOI：
10.1090/s0025-5718-01-01413-2
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
Z. Belhachmi;F. B. Belgacem
中科院分区：
文献类型：
--
作者：
Z. Belhachmi;F. B. Belgacem
与线性有限元相比，将高阶有限元应用于单向接触变分不等式可以提供更精确的计算解。到目前为止，对他们表现的数学研究还没有取得重大进展。主要的问题是在接触区的离散解上模拟非侵彻的西诺里尼条件。在这项工作中，我们描述了泊松-西诺里尼问题的两个非协调二次有限元逼近。针对易于实现这一关键的现实问题，我们给出了其效率的数值分析。利用Falk引理，我们根据精确解的正则性证明了最优和准最优收敛速度。
Applying high order finite elements to unilateral contact variational inequalities may provide more accurate computed solutions, compared with linear finite elements. Up to now, there was no significant progress in the mathematical study of their performances. The main question is involved With the modeling of the nonpenetration Signorini condition on the discrete solution along the contact region. In this work we describe two nonconforming quadratic finite element approximations of the Poisson-Signorini problem. responding to the crucial practical concern of easy implementation, and we present the numerical analysis of their efficiency. By means of Falk's Lemma we prove optimal and quasi-optimal convergence rates according to the regularity of the exact solution.