This paper aims to contribute with a hierarchically enhanced recovery-based error estimator by using the Zienkiewicz–Zhu (ZZ) recovery procedure and a generalized finite element formulation. The proposed stress recovery consists in an approximation procedure that is enriched hierarchically by using partition of unity (PU) and an enrichment function. In other words, the approximation matrix used for stress field recovery employs the enriched finite element (FE) shape function. Furthermore, the edge-bubble hierarchically enriched strategy in the context of a generalized finite element approach is adopted to develop the enriched $$\hbox {C}^{0}$$ C 0 element and approximation the matrix. The error estimator based on this hierarchically enhanced recovery procedure and the generalized finite element approach is employed to solve several elastic and elastoplastic hardening benchmark problems. Moreover, the effectivity index, refinement index, recovered stress field, global error and local error, both in energy norm, are evaluated in several applications. In addition, the sensitivity of the proposed recovery procedure to a severely distorted mesh is also analysed. The results obtained by the proposed procedure is compared to other well-established recovery procedures and finite element approaches. By comparing the results, the robustness in the numerical performance, the versatility in the computational implementation and the competitivity of the proposed procedure are demonstrated in the applications.

中文翻译：

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一种基于层次增强恢复的基于广义有限元方法的二维弹塑性建模误差估计器

本文旨在通过使用 Zienkiewicz-Zhu (ZZ) 恢复程序和广义有限元公式，提供基于分层增强的恢复的误差估计器。建议的应力恢复包括一个近似程序，该程序通过使用统一分区 (PU) 和富集函数分层富集。换言之，用于应力场恢复的近似矩阵采用了丰富的有限元 (FE) 形状函数。此外，采用广义有限元方法上下文中的边缘气泡分层丰富策略来开发丰富的 $$\hbox {C}^{0}$$ C 0 元素并逼近矩阵。采用基于这种分层增强恢复程序和广义有限元方法的误差估计器来解决几个弹性和弹塑性硬化基准问题。此外，在多个应用中评估了能量范数中的有效性指数、细化指数、恢复应力场、全局误差和局部误差。此外，还分析了建议的恢复程序对严重扭曲网格的敏感性。将建议程序获得的结果与其他完善的恢复程序和有限元方法进行比较。通过比较结果，在应用中证明了数值性能的稳健性、计算实现的多功能性和所提出的程序的竞争力。