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Analysis of adaptive finite element methods for −εU″+U′=F based on a-posteriori error estimates

Part I: Theory of Singular Perturbations

Part of the Lecture Notes in Mathematics book series (LNM,volume 942)

Abstract

A-posteriori error estimates containing realistic bounds provide a basis for adaptive numerical methods solving differential equations. In this paper, for a singularly perturbed convection-diffusion model problem, a finite element method is analysed which is based on a technique of approximate symmetrization of the given unsymmetric problem. Realistic a-posteriori error estimates with respect to an appropriate energy-norm are presented. A series of numerical examples demonstrate that our adaptive methods detect and resolve the boundary layer.

Keywords

  • Finite Element Method
  • Mesh Refinement
  • Unique Solvability
  • Finite Element Approximation
  • Finite Element Solution

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1982 Springer-Verlag

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Reinhardt, HJ. (1982). Analysis of adaptive finite element methods for −εU″+U′=F based on a-posteriori error estimates. In: Eckhaus, W., de Jager, E.M. (eds) Theory and Applications of Singular Perturbations. Lecture Notes in Mathematics, vol 942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094749

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  • DOI: https://doi.org/10.1007/BFb0094749

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11584-7

  • Online ISBN: 978-3-540-39332-0

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