Error estimation and adaptive procedures based on superconvergent patch recovery (SPR) techniques

Wiberg, Nils‐Erik; Abdulwahab, Fethi; Li, Xiangdong

doi:10.1007/bf02913818

Cited by 24 publications

(16 citation statements)

References 45 publications

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“…The use of gradient recovery or other averaging strategies for evolution problems in the engineering literature was pioneered by Wiberg et al [32]. Leykekhman and Wahlbin [33] used local parabolic estimates to extend the framework to cover parabolic problems, showing that the recovered gradient estimated the local element error accurately, provided the temporal error was higher order.…”

Section: Evolution and Other Problemsmentioning

confidence: 99%

Flexible patch post‐processing recovery strategies for solution enhancement and adaptive mesh refinement

Carey

2011

Numerical Meth Engineering

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SUMMARYThis study considers local post-processing strategies on contiguous patches of cells (or elements) and the properties and applications of the resulting approximations. For instance, one is interested in accuracy of recovered gradients and in their use in constructing error estimators or error indicators for adaptivity. Hence, there are two distinct concepts: (1) The improved quality of recovered gradients on a local patch; and/or (2) the use of local recovered quantities to construct error indicators to guide adaptive refinement schemes. We present a framework generalizing existing strategies for averaging operators and discuss the advantages of this framework in a parallel computing environment.

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Section: Evolution and Other Problemsmentioning

confidence: 99%

Flexible patch post‐processing recovery strategies for solution enhancement and adaptive mesh refinement

Carey

2011

Numerical Meth Engineering

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“…The evaluation of the second derivatives of at the Gauss points of linear elements can be performed by nodal projection and smoothing of the first derivatives field [37,38].…”

Section: Computation Of the Characteristic Length Vectormentioning

confidence: 99%

Possibilities of finite calculus in computational mechanics

Oñate

2004

Numerical Meth Engineering

106

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SUMMARYThe expression 'finite calculus' refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a space-time domain of finite size. The governing equations resulting from this approach are different from those of infinitesimal calculus theory and they incorporate new terms which depend on the dimensions of the balance domain.The new governing equations allow the derivation of naturally stabilized numerical schemes using any discretization procedure. The paper discusses the possibilities of the finite calculus method for the finite element solution of convection-diffusion problems with sharp gradients, incompressible fluid flow and incompressible solid mechanics problems and strain localization situations.

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“…For the transfer between non-matching meshes, this discontinuity can regarded as a weakness of the transfer operator. Therefore, nodal patches have been extensively used in literature [12,25,[33][34][35] to build continuous interpolations. The method often comes down to calculating nodal valuesσ k of the recovered fieldσ at any node k of the mesh, and then to interpolating (15) these values with the continuous interpolation functions N of the finite element mesh, e.g.…”

Section: Recovery By Nodal Patches (Avg Ls Spr)mentioning

confidence: 99%

Parallel, second-order and consistent remeshing transfer operators for evolving meshes with superconvergence property on surface and volume

Kumar¹,

Fourment²,

Guerdoux³

2015

Finite Elements in Analysis and Design

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Error estimation and adaptive procedures based on superconvergent patch recovery (SPR) techniques

Cited by 24 publications

References 45 publications

Flexible patch post‐processing recovery strategies for solution enhancement and adaptive mesh refinement

Flexible patch post‐processing recovery strategies for solution enhancement and adaptive mesh refinement

Possibilities of finite calculus in computational mechanics

Parallel, second-order and consistent remeshing transfer operators for evolving meshes with superconvergence property on surface and volume

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