Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order

Yuan, Songmei; Qiu, Xing; Wang, Xu; Ye, Kangsheng

doi:10.1007/s10483-008-0504-8

Cited by 9 publications

(9 citation statements)

References 8 publications

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“…Note that once Eq. (7) (8) is not satisfied, the error-averaging method (Yuan et al, 2008) is used to subdivide each into two elements, forming a new refined mesh, as described in Section 5. Then the procedure returns to the first step (i.e.…”

Section: Outline Of the Solution Proceduresmentioning

confidence: 99%

“…This subdivision approach is called the error-averaging method (Yuan et al, 2008), with the areas of error squared on the two sides of point a j roughly equal to each other. yet be accurate enough, and so the procedure continues to adjust the bounds until Eq.…”

Section: Elememt Subdivisionmentioning

confidence: 99%

“…These EEP solutions are then used as if they were exact solutions to estimate the errors in the FE solutions and hence to further guide mesh refinements Yuan et al, 2008). This yields a simple, efficient, reliable and general adaptive FE procedure that is able to find sufficiently fine meshes for the accuracy of the obtained FE solutions to satisfy the user-preset error tolerances on both eigenvalues and eigenfunctions.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive finite element method for eigensolutions of regular second and fourth order Sturm-Liouville problems via the element energy projection technique

Yuan

Wang

et al. 2017

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FindingsNumerical results for a number of representative and challenging SL problems are presented to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method. Research limitationsThe method is limited to regular SL problems, but it can also solve some singular SL problems in an indirect way. ValueComprehensive utilization of the EEP technique yields a simple, efficient and reliable adaptive FE procedure that finds sufficiently fine meshes for preset error tolerances on eigenvalues and eigenfunctions to be achieved, even on problems which proved troublesome to competing methods. The method can readily be extended to vector SL problems.

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Section: Outline Of the Solution Proceduresmentioning

confidence: 99%

Section: Elememt Subdivisionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive finite element method for eigensolutions of regular second and fourth order Sturm-Liouville problems via the element energy projection technique

Yuan

Wang

et al. 2017

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“…This estimation tends to become more and more accurate as the mesh becomes finer and finer. The strategy therefore allows ambitious development [11,12] of a very efficient and reliable adaptive procedure with the goal being, for a user-specified tolerance Tol, to find a proper mesh such that the FE solution V ℎ on satisfies the maximum norm criterion [12]:…”

Section: Adaptive Scheme For Linear Problemsmentioning

confidence: 99%

An Adaptive FEM for Buckling Analysis of Nonuniform Bernoulli-Euler Members via the Element Energy Projection Technique

Yuan

Wang

2013

Mathematical Problems in Engineering

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This paper presents a new adaptive finite element (FE) procedure for accurate, efficient, and reliable computation of the critical buckling loads and the associated modes of nonuniform Bernoulli-Euler members. After the conventional FE solution on a given mesh has been obtained, a novel conceptual and practical strategy is introduced, in which the FE solution of the eigenproblem is equivalently viewed as the FE solution of an associated linear problem. This strategy allows the recently developed element energy projection (EEP) technique to be readily used to calculate super-convergent FE solutions for buckling modes, which are subsequently used to estimate the FE solution errors and to further guide mesh refinements, until the accuracy of the FE solution matches the user-preset error tolerance. Numerical examples are given to show the effectiveness, efficiency, accuracy, and reliability of the proposed method, which also paves the way for development of an adaptive FE solver for more general and complicated eigenproblems.

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“…A number of research studies have been conducted on this subject [32,33]. In recent years, a super-convergence technique named Element Energy Projection (EEP) method was proposed by Yuan et al [34][35][36]. Its core assumption is to assume the energy projection theorem in the FEM mathematical theory [37] to be almost true for a single element.…”

Section: Introductionmentioning

confidence: 99%

Application of Finite Layer Method in Pavement Structural Analysis

et al. 2017

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Abstract:The finite element (FE) method has been widely used in predicting the structural responses of asphalt pavements. However, the three-dimensional (3D) modeling in general-purpose FE software systems such as ABAQUS requires extensive computations and is relatively time-consuming. To address this issue, a specific computational code EasyFEM was developed based on the finite layer method (FLM) for analyzing structural responses of asphalt pavements under a static load. Basically, it is a 3D FE code that requires only a one-dimensional (1D) mesh by incorporating analytical methods and using Fourier series in the other two dimensions, which can significantly reduce the computational time and required resources due to the easy implementation of parallel computing technology. Moreover, a newly-developed Element Energy Projection (EEP) method for super-convergent calculations was implemented in EasyFEM to improve the accuracy of solutions for strains and stresses over the whole pavement model. The accuracy of the program is verified by comparing it with results from BISAR and ABAQUS for a typical asphalt pavement structure. The results show that the predicted responses from ABAQUS and EasyFEM are in good agreement with each other. The EasyFEM with the EEP post-processing technique converges faster compared with the results derived from ordinary EasyFEM applications, which proves that the EEP technique can improve the accuracy of strains and stresses from EasyFEM. In summary, the EasyFEM has a potential to provide a flexible and robust platform for the numerical simulation of asphalt pavements and can easily be post-processed with the EEP technique to enhance its advantages.

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Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order

Cited by 9 publications

References 8 publications

Adaptive finite element method for eigensolutions of regular second and fourth order Sturm-Liouville problems via the element energy projection technique

Adaptive finite element method for eigensolutions of regular second and fourth order Sturm-Liouville problems via the element energy projection technique

An Adaptive FEM for Buckling Analysis of Nonuniform Bernoulli-Euler Members via the Element Energy Projection Technique

Application of Finite Layer Method in Pavement Structural Analysis

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