Postprocessing techniques and h-adaptive finite element-eigenproblem analysis

Baušys, Romualdas; Hager, Patrik; Wiberg, Nils‐Erik

doi:10.1016/s0045-7949(01)00051-7

Cited by 4 publications

(3 citation statements)

References 16 publications

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“…At the end of the 1990s Wiberg and coworkers published a series of papers on adaptive methods for natural vibrations [22][23][24][25]. They developed Superconvergent Patch Recovery based method for eigenfrequency error evaluation.…”

Section: State Of Knowledgementioning

confidence: 99%

On some hp -adaptive finite element method for natural vibrations

Jasiński

Zboiński

2013

Computers & Mathematics with Applications

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Section: State Of Knowledgementioning

confidence: 99%

On some hp -adaptive finite element method for natural vibrations

Jasiński

Zboiński

2013

Computers & Mathematics with Applications

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“…The same example is considered in [9,30] where mesh adaptivity aiming at reducing global measures of the error are considered. Although the examples shown therein refer to lower wave numbers, a close comparison with the results obtained with the goal-oriented strategy presented in this work reveals that our technique properly resolves the singularities of the primal problem (refining the regions of the domain where the primal error is larger) while refining, at the same time, the areas relevant for the quantity of interest.…”

Section: Car Cavitymentioning

confidence: 99%

Goal-oriented h-adaptivity for the Helmholtz equation: error estimates, local indicators and refinement strategies

2011

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This paper introduces a new goal-oriented adaptive technique based on a simple and effective post-process of the finite element approximations. The goal-oriented character of the estimate is achieved by analyzing both the direct problem and an auxiliary problem, denoted as adjoint or dual problem, which is related to the quantity of interest. Thus, the error estimation technique proposed in this paper would fall into the category of recovery-type explicit residual a posteriori error estimates. The procedure is valid for general linear quantities of interest and it is also extended to non-linear ones. The numerical examples demonstrate the efficiency of the proposed approach and discuss: (1) different error representations, (2) assessment of the dispersion error, and (3) different remeshing criteria.

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“…Country Date lized in the monograph [234]) and to optimization [235-23 8]. Prof R. Bausys is investigating the applied strategies of generating the finite element network of structural mechanics, etc [239][240][241][242]. Other recent investigations of the Department are connected with developing finite elements for plates and shells.…”

Section: Scientistmentioning

confidence: 99%

Aleksandras Čyras and Optimization in Structural Mechanics

Atkočiūnas

Čižas

2002

Journal of Civil Engineering and Management

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The study describes how in Lithuania (mostly in Vilnius) during some past decades a new trend of investigations in structural mechanics thanks to Aleksandras Čyras' (1927–2001) research and organisational activities has been developed. The main distinguished features of the trend are: application of mathematical programming, and especially the duality theory, to the optimization of elastic-plastic and other structures, formulation of mathematical models of structural mechanics problems, elaborating algorithms and programmes for their solution. The advantages of the research results are shown, a large information concerning the publication of the results and the evolution of investigations initiated by A. Čyras are presented.

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Postprocessing techniques and h-adaptive finite element-eigenproblem analysis

Cited by 4 publications

References 16 publications

On some hp -adaptive finite element method for natural vibrations

On some hp -adaptive finite element method for natural vibrations

Goal-oriented h-adaptivity for the Helmholtz equation: error estimates, local indicators and refinement strategies

Aleksandras Čyras and Optimization in Structural Mechanics

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