A Nitsche method for the elastoplastic torsion problem

IF 1.9 3区 数学 Q2 Mathematics
F. Chouly, T. Gustafsson, P. Hild
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引用次数: 1

Abstract

This study is concerned with the elastoplastic torsion problem, in dimension $n\geq1$, and in a polytopal, convex or not, domain. In the physically relevant case where the source term is a constant, this problem can be reformulated using the distance function to the boundary. We combine the aforementioned reformulation  with a Nitsche-type discretization as in [Burman, Erik, et al. Computer Methods in Applied Mechanics and Engineering 313 (2017): 362-374]. This has two advantages: 1) it leads to optimal error bounds in the natural norm, even for nonconvex domains; 2) it is easy to implement within most of finite element libraries. We establish the well-posedness and convergence properties of the method, and illustrate its behavior with numerical experiments.
弹塑性扭转问题的Nitsche方法
本研究涉及的弹塑性扭转问题,在尺寸$n\geq1$,并在一个多边形,凸或非,域。在物理相关的情况下,源项是一个常数,这个问题可以用到边界的距离函数重新表述。我们将上述重新表述与nitsche型离散化结合起来,如[Burman, Erik, et al.]。应用力学与工程计算机方法[j].应用力学与工程计算机方法[13](2017):362-374。这有两个优点:1)它导致自然范数的最优误差界,即使对于非凸域;2)在大多数有限元库中易于实现。建立了该方法的适定性和收敛性,并用数值实验说明了该方法的性能。
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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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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