Improved element stresses for node and element patches using superconvergent patch recovery

Wiberg, Nils‐Erik; Abdulwahab, Fethi; Ziukas, Saulius

doi:10.1002/cnm.1640110708

Cited by 23 publications

(14 citation statements)

References 7 publications

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“…In Reference 5, the displacement ®eld was interpolated instead of stress, and thus essential boundary residuals were required to be added to the least square functional. Wiberg et al 6 also presented a stress based element patch with quadratic weight functions for QUAD4 elements and showed that the extracted results compared to that in Reference 3. In addition to these, Wiberg and Li 7 also published a displacement ®eld based extraction process which was essentially almost similar to the work in Reference 5.…”

Section: Introductionmentioning

confidence: 84%

A weighted element patch based superconvergent stress extraction strategy

Mukherjee

Krishnamoorthy

1998

Commun. Numer. Meth. Engng.

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SUMMARYA superconvergent element patch based stress extraction strategy is proposed for general FE postprocessing and/or error estimation procedures in adaptive ®nite element analysis. Generalized weight functions are proposed for discrete least-square functionals, and a corrected conjoint polynomial ®tting procedure is presented to ensure accurate stress extraction from the element domain once the primary level stress parameters have been evaluated. A numerical example is presented to ®x the parameters of the weight functions. Several plane stress examples are solved using QUAD4 elements, and results are compared to those of the node patch based extraction method using the conventional conjoint polynomial method. It is shown that the proposed technique yields more accurate results with enhanced local convergence. Although the method may be applied to higher-order elements too, only QUAD4 elements are chosen for the present examples since the present secondary re®tting strategy assumes superconvergent points only to be at element centroids. #

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Section: Introductionmentioning

confidence: 84%

A weighted element patch based superconvergent stress extraction strategy

Mukherjee

Krishnamoorthy

1998

Commun. Numer. Meth. Engng.

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“…Whenever they are not satisfied, a regularization term is added to the least square functional presented in Section 3.3.2 and Eq. (27). The value of the β coefficient of (27) is iteratively increased till the constraints of (29) are satisfied.…”

Section: Engineering Issuementioning

confidence: 99%

“…On the other hand, in a Lagrangian formulation with complete remeshing, some parts of the domain are very often only weakly changed by remeshing. Therefore, in order to minimize diffusion resulting from usual transfer techniques, interpolation can be avoided through a direct calculation of recovered fields on element patches, as for instance in [27,29]. Element patches, P g , are built on the old mesh.…”

Section: Superconvergent Recovery By Element Patches (Epr1 and Epr2)mentioning

confidence: 99%

“…Gu et al [26] modified SPR by using integration points as sampling points and introducing additional nodes, which increased the performance of SPR for nonlinear problems remarkably. Wiberg et al [27,28] presented an improvement to SPR by extending the technique to use element patches rather than nodal patches, and extended the SPR to SPRE (penalizing the violation of the equilibrium) and SPREB (by including a least square fit of the boundary conditions). SPR technique has been more often used for the purpose of FEM error estimation rather than remapping.…”

Section: Introductionmentioning

confidence: 98%

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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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“…A more appropriate way of expressing M* over an element is by directly weighting the patch solution. 7 The error estimate (8) is used in the adaptive procedure to obtain an optimum mesh in which the error is equally distributed over the elements in a mesh; see Reference 8.…”

Section: The Superconvergent Patch Recovery and Error Estimationmentioning

confidence: 99%

Superconvergent Patch Recovery in Problems of Mixed Form

Wiberg

Abdulwahab

1997

Commun. Numer. Meth. Engng.

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SUMMARYThe superconvergent patch recovery (SPR technique) has been shown to be an eective postprocessing procedure in which an improved solution is obtained based on the original ®nite element solution. The technique was applied to second order problems with success, but the method has not yet been studied on problems posed in mixed form. This paper demonstrates that the technique can be applied to beam and plate bending problems, characterized by fourth order dierential equations. The dierential equation is here written as two coupled dierential equations of second order leading to a mixed ®nite element procedure based on approximations of the moment and displacement ®elds. Two elements of mixed type are handled, namely a triangular plate element with constant moment ®eld and a rectangular element with linearly varying bending moments. Numerical examples are given to show that the postprocessed solution is more accurate and has a higher rate of convergence.

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Improved element stresses for node and element patches using superconvergent patch recovery

Cited by 23 publications

References 7 publications

A weighted element patch based superconvergent stress extraction strategy

A weighted element patch based superconvergent stress extraction strategy

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

Superconvergent Patch Recovery in Problems of Mixed Form

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