Adaptive finite element strategies based on error assessment

Huerta, Antonio; Ferran, Antonio Rodríguez; Dı́ez, Pedro; Sarrate, Josep

doi:10.1002/(sici)1097-0207(19991210)46:10<1803::aid-nme725>3.0.co;2-3

Cited by 68 publications

(22 citation statements)

References 33 publications

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“…Otherwise, we assume that the error is equally distributed over the elements and use the LB criterion to obtain the new element area: (10) in which N represents the total number of elements in the old mesh and p is the polynomial order of the approximation. Since this method estimates the error using a global quantity, the energy norm, it cannot be used to control the error in local quantities of interest, such as a specific component of stress or strain.…”

Section: Error Estimatormentioning

confidence: 99%

“…The h-adaptive FE strategy subdivides the integration region into successively smaller sub-regions [10], thus changing the density of the elements to yield a more accurate solution while keeping the element order constant. In the case of small deformations, where the mesh geometry does not change throughout the solution process, the h-adaptive method can be used to generate a better mesh at the end of the analysis with a repeated analysis being expected to improve the solution accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Refined h-adaptive finite element procedure for large deformation geotechnical problems

et al. 2011

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Adaptive finite element procedures automatically refine, coarsen, or relocate elements in a finite element mesh to obtain a solution with a specified accuracy. Although a significant amount of research has been devoted to adaptive finite element analysis, this method has not been widely applied to nonlinear geotechnical problems due to their complexity. In this paper, the h-adaptive finite element technique is employed to solve some complex geotechnical problems involving material nonlinearity and large deformations. The key components of h-adaptivity including robust mesh generation algorithms, error estimators and remapping procedures are discussed. This paper includes a brief literature review as well as formulation and implementation details of the h-adaptive technique. Finally, the method is used to solve some classical geotechnical problems and results are provided to illustrate the performance of the method.

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Section: Error Estimatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Refined h-adaptive finite element procedure for large deformation geotechnical problems

et al. 2011

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“…[3,19]). Such strategies focus the computation work on the parts of the structure which are highly stressed and where the discretization error is maximum.…”

Section: Introductionmentioning

confidence: 99%

Three dimensional automatic refinement method for transient small strain elastoplastic finite element computations

et al. 2011

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“…Whilst mesh adaptivity can be used with a finite difference model (Blayo and Debreu 1999), its use is far more common in finite element and finite volume models, which can easily employ unstructured meshes. In such a context, adaptive meshing can lead to not only an improvement in solution quality, but also in the discovery of features that would be disguised by a fixed mesh (Huerta et al 1999). The use of this new, still developing technology, is sufficiently challenging that we are forced to use a vastly simplified model domain.…”

Section: Introductionmentioning

confidence: 99%

Idealised flow past an island in a dynamically adaptive finite element model

2010

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The problem of flow separation around islands is investigated using a dynamically adaptive finite element model to allow for resolution of the shear layers that form in the advent of separation. The changes in secondary circulation and vertical motion that occur in both attached and separated flows are documented, as is the degree of closure of the wake eddies. In the numerical experiments presented, the strongest motion always takes place at the sides of the idealised island, where flow curvature and shear act together to induce ascent. In contrast, it is the slower motion within the wake eddies that allow streamlines to extend from the bottom to the surface. We find no evidence for closure of the wake eddies. Rather, all of our separated experiments show that streamlines that pass through the eddies originate outside of the shear layers and frictional boundary layers on the upstream side of the idealised island. The numerical experiments demonstrate the potential for dynamically adaptive, unstructured meshes to resolve the separated shear layers that occur downstream of the idealised island, as well as the narrow boundary layers that form on the island itself.

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Adaptive finite element strategies based on error assessment

Cited by 68 publications

References 33 publications

Refined h-adaptive finite element procedure for large deformation geotechnical problems

Refined h-adaptive finite element procedure for large deformation geotechnical problems

Three dimensional automatic refinement method for transient small strain elastoplastic finite element computations

Idealised flow past an island in a dynamically adaptive finite element model

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