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M Aurada1, M Feischl, M Karkulik

  • 1Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria.

Engineering Analysis with Boundary Elements
|February 21, 2012
PubMed
Summary

This study adapts error estimators for stable Johnson-Nédélec coupling in boundary element method (BEM) and finite element method (FEM) simulations. Numerical experiments guide adaptive algorithms, comparing the effectiveness of various error estimation techniques.

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Area of Science:

  • Computational Mathematics
  • Numerical Analysis
  • Scientific Computing

Background:

  • The Johnson-Nédélec one-equation approach offers a stable coupling of the finite element method (FEM) and boundary element method (BEM).
  • Prior analytical results for error estimation in symmetric FEM-BEM coupling exist.
  • Adapting these estimators to the Johnson-Nédélec coupling is a novel research direction.

Purpose of the Study:

  • To adapt existing a posteriori error estimates for the Johnson-Nédélec FEM-BEM coupling.
  • To analyze the performance of weighted-residual, two-level, and (h-h/2)-based error estimators.
  • To utilize these estimators for steering adaptive algorithms and comparing their effectivity.

Main Methods:

  • Adaptation of analytical results for a posteriori error estimates.
  • Analysis of weighted-residual error estimators.
  • Analysis of two-level error estimators.
  • Analysis of (h-h/2)-based error estimators.
  • Numerical experiments to steer h-adaptive algorithms.

Main Results:

  • The study successfully adapted various a posteriori error estimators for the Johnson-Nédélec coupling.
  • Numerical experiments demonstrated the utility of these estimators in guiding adaptive mesh refinement.
  • Comparative analysis provided insights into the effectivity of different error estimation strategies.

Conclusions:

  • The adapted error estimators are effective for the Johnson-Nédélec FEM-BEM coupling.
  • The choice of error estimator can significantly impact the performance of adaptive algorithms.
  • This work provides a foundation for more efficient and accurate numerical simulations using coupled FEM-BEM methods.

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