On the role of enrichment and statical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods
On the role of enrichment and statical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods
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关于恢复场的丰富和静态容许性在丰富有限元方法的后验误差估计中的作用
DOI：
10.1108/02644401211271609
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发表时间：
2012
影响因子：
1.6
通讯作者：
Andrés González-Estrada O
中科院分区：
文献类型：
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作者：
Andrés González-Estrada O
目的——本文的目的是评估恢复解的静态容许性的影响以及恢复解代表奇异解的能力；还有丰富的有限元方法（例如扩展有限元方法，XFEM）的基于恢复的误差估计器的准确性、局部和全局有效性。设计/方法/途径——作者研究了两种恢复技术的性能。第一个是最近开发的具有平衡和富集功能的超收敛补丁恢复程序（SPR-CX）。第二种称为扩展移动最小二乘恢复 (XMLS)，它丰富了恢复的解决方案，但不强制平衡约束。两者都是扩展恢复技术，因为恢复过程中使用的多项式基都用奇异项进行了丰富，以便更好地描述解决方案的奇异性质。结果-将两种技术的收敛性和有效性指数与未经丰富增强所获得的结果进行比较的数值结果清楚地表明，在解决此类问题的 Zienkiewicz-Zhu 型误差估计器中需要使用扩展恢复技术。结果还揭示了静态可接受的恢复解所产生的有效性的显着提高。原创性/价值——本文表明，扩展恢复程序和静态可接受性都是准确评估丰富的有限元近似质量的关键。
Purpose–The purpose of this paper is to assess the effect of the statical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also the accuracy, local and global effectivity of recovery‐based error estimators for enriched finite element methods (e.g. the extended finite element method, XFEM).Design/methodology/approach–The authors study the performance of two recovery techniques. The first is a recently developed superconvergent patch recovery procedure with equilibration and enrichment (SPR‐CX). The second is known as the extended moving least squares recovery (XMLS), which enriches the recovered solutions but does not enforce equilibrium constraints. Both are extended recovery techniques as the polynomial basis used in the recovery process is enriched with singular terms for a better description of the singular nature of the solution.Findings–Numerical results comparing the convergence and the effectivity index of both techniques with those obtained without the enrichment enhancement clearly show the need for the use of extended recovery techniques in Zienkiewicz‐Zhu type error estimators for this class of problems. The results also reveal significant improvements in the effectivities yielded by statically admissible recovered solutions.Originality/value–The paper shows that both extended recovery procedures and statical admissibility are key to an accurate assessment of the quality of enriched finite element approximations.