On some new recovery-based a posteriori error estimators

Maisano, G; Micheletti, Stefano; Perotto, Simona; Bottasso, Carlo L.

doi:10.1016/j.cma.2005.07.024

Cited by 28 publications

(15 citation statements)

References 22 publications

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“…z s z t is a symmetric positive semidefinite matrix, with s,t = 1, 2 and (z 1 , z 2 ) ∈ [L 2 (Ω)] 2 , and ∆ K is the patch of elements associated with K. According to [33,34], E ∇ coincides with the difference between the discrete gradient of the density, ∇ρ h , and a corresponding suitable reconstruction, P(∇ρ h ). In the literature, several examples for the recovery operator P are available (see, e.g., [16,19,25,33,34]), which consists of a projection or an average of the discrete gradient across a suitable patch of elements surrounding K. We adopt the area-weighed average over the patch ∆ K ,…”

Section: The Theoretical Background: An Anisotropic Error Analysismentioning

confidence: 99%

Adaptive Topology Optimization for Innovative 3D Printed Metamaterials

Cristofaro¹,

Galimberti²,

Bianchi³

et al. 2021

14th WCCM-ECCOMAS Congress

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An adaptive method for designing the infill pattern of 3D printed objects is proposed. In particular, new unit cells for metamaterials are designed in order to match prescribed mechanical specifications. To this aim, we resort to topology optimization at the microscale driven by an inverse homogenization to guarantee the desired properties at the macroscale. The whole procedure is additionally enriched with an anisotropic adaptive generation of the computational mesh. The proposed algorithm is first numerically verified both in a mono-and in a multi-objective context. Then, a mechanical validation and 3D manufacturing through fused-model-deposition are carried out to assess the feasibility of the proposed design workflow. 1 MOTIVATIONS Recently, the developing of innovative manufacturing technologies has involved the industry in numerous fields (e.g., automotive, aerospace, medical industry) [4, 23]. Among the different innovations, the Additive Manufacturing (AM) has revolutionized the way to think the production [2]. In fact, the AM has allowed the production of objects with complex geometries in a simple way, overcoming the constraints

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Section: The Theoretical Background: An Anisotropic Error Analysismentioning

confidence: 99%

Adaptive Topology Optimization for Innovative 3D Printed Metamaterials

Cristofaro¹,

Galimberti²,

Bianchi³

et al. 2021

14th WCCM-ECCOMAS Congress

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“…Several recipes are available in the literature with the aim of improving the effectiveness of the recovery procedure (see, e.g., [29][30][31][32]). Although the theoretical properties of these recovery procedures are not yet very well understood [31,[33][34][35][36], recovery-based error estimators show an astonishing numerical robustness, heuristically assessed on different problem settings (see, e.g., [32,[37][38][39]). The main advantage of these estimators is the computational cheapness as well as the easiness of implementation: they do not involve any other quantity except for the solution and the corresponding gradient.…”

Section: An Anisotropic Recovery-based Error Estimatormentioning

confidence: 99%

Anisotropic mesh adaptation driven by a recovery‐based error estimator for shallow water flow modeling

Porta

Perotto

Ballio

2011

Numerical Methods in Fluids

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SUMMARY The aim of this paper is to propose an effective anisotropic mesh adaptation procedure for the solution of the shallow water equations. The hyperbolic partial differential equation system is solved via the streamline diffusion FEM, suitably modified by a shock‐capturing correction. The proposed adaptation procedure relies on a recovery‐based error estimator. In particular, we look for an anisotropic error estimator able to select not only the size but also the shape and the orientation of the mesh elements, with the aim of optimizing the computational advantages yielded by a standard isotropic mesh adaptation strategy. The robustness of the proposed estimator is assessed when either a single physical quantity, meaningful for the problem at hand, or a combination of all the shallow water system components drives the adaptation procedure. For this purpose, steady shallow water problems as well as unsteady configurations are considered. Copyright © 2011 John Wiley & Sons, Ltd.

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“…The proposed error estimator is reminiscent of the Zienkiewicz-Zhu (ZZ) error estimator which is a frequently used tool for the a posteriori finite element error analysis and which enjoys a high popularity in engineering because of its striking simplicity and universality [39]. Some ZZ-type error estimators have been developed for various applications of the FEM over the last two decades [12,13,[40][41][42]. Efficiency and reliability of these estimators have also been analyzed either by numerical experimentation, mathematical theory, or both.…”

Section: Introductionmentioning

confidence: 99%

On error estimator and adaptivity in the meshless Galerkin boundary node method

2011

Comput Mech

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In this article, a simple a posteriori error estimator and an effective adaptive refinement process for the meshless Galerkin boundary node method (GBNM) are presented. The error estimator is formulated by the difference between the GBNM solution itself and its L 2 -orthogonal projection. With the help of a localization technique, the error is estimated by easily computable local error indicators and hence an adaptive algorithm for h-adaptivity is formulated. The convergence of this adaptive algorithm is verified theoretically in Sobolev spaces. Numerical examples involving potential and elasticity problems are also provided to illustrate the performance and usefulness of this adaptive meshless method.

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On some new recovery-based a posteriori error estimators

Cited by 28 publications

References 22 publications

Adaptive Topology Optimization for Innovative 3D Printed Metamaterials

Adaptive Topology Optimization for Innovative 3D Printed Metamaterials

Anisotropic mesh adaptation driven by a recovery‐based error estimator for shallow water flow modeling

On error estimator and adaptivity in the meshless Galerkin boundary node method

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