A posteriori pointwise error estimates for the boundary element method

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This report presents a new approach for a posteriori pointwise error estimation in the boundary element method. The estimator relies upon the evaluation of hypersingular integral equations, and is therefore intrinsic to the boundary integral equation approach. This property allows some theoretical justification by mathematically correlating the exact and estimated errors. A methodology is developed for approximating the error on the boundary as well as in the interior of the domain. In the interior, error estimates for both the function and its derivatives (e.g. potential and interior gradients for potential problems, displacements and stresses for elasticity problems) are presented. Extensive ... continued below

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39 p.

Creation Information

Paulino, G.H.; Gray, L.J. & Zarikian, V. January 1, 1995.

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This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this report can be viewed below.

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  • Paulino, G.H. Cornell Univ., Ithaca, NY (United States). School of Civil and Environmental Engineering
  • Gray, L.J. Oak Ridge National Lab., TN (United States)
  • Zarikian, V. Univ. of Central Florida, Orlando, FL (United States). Dept. of Mathematics

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Description

This report presents a new approach for a posteriori pointwise error estimation in the boundary element method. The estimator relies upon the evaluation of hypersingular integral equations, and is therefore intrinsic to the boundary integral equation approach. This property allows some theoretical justification by mathematically correlating the exact and estimated errors. A methodology is developed for approximating the error on the boundary as well as in the interior of the domain. In the interior, error estimates for both the function and its derivatives (e.g. potential and interior gradients for potential problems, displacements and stresses for elasticity problems) are presented. Extensive computational experiments have been performed for the two dimensional Laplace equation on interior domains, employing Dirichlet and mixed boundary conditions. The results indicate that the error estimates successfully track the form of the exact error curve. Moreover, a reasonable estimate of the magnitude of the actual error is also obtained.

Physical Description

39 p.

Notes

OSTI as DE95008099

Source

  • Other Information: PBD: Jan 1995

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  • Other: DE95008099
  • Report No.: ORNL/TM--12820
  • Grant Number: AC05-84OR21400
  • DOI: 10.2172/42836 | External Link
  • Office of Scientific & Technical Information Report Number: 42836
  • Archival Resource Key: ark:/67531/metadc686673

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Creation Date

  • January 1, 1995

Added to The UNT Digital Library

  • July 25, 2015, 2:20 a.m.

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  • Aug. 25, 2016, 2:42 p.m.

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Paulino, G.H.; Gray, L.J. & Zarikian, V. A posteriori pointwise error estimates for the boundary element method, report, January 1, 1995; Tennessee. (digital.library.unt.edu/ark:/67531/metadc686673/: accessed September 26, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.