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Gradient Recovery for Singularly Perturbed Boundary Value Problems I: One-Dimensional Convection-Diffusion

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Abstract

We consider a Galerkin finite element method that uses piecewise linears on a class of Shishkin-type meshes for a model singularly perturbed convection-diffusion problem. We pursue two approaches in constructing superconvergent approximations of the gradient. The first approach uses superconvergence points for the derivative, while the second one combines the consistency of a recovery operator with the superconvergence property of an interpolant. Numerical experiments support our theoretical results.

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Authors and Affiliations

  1. Institut für Numerische Mathematik Technische Universität Dresden D-01062 Dresden Germany e-mail: >roos,torsten<@math.tu-dresden.de, , , , , , DE

    Hans-Görg Roos & Torsten Linß

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  1. Hans-Görg Roos
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  2. Torsten Linß
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Received November 12, 1999; revised September 9, 2000

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Roos, HG., Linß, T. Gradient Recovery for Singularly Perturbed Boundary Value Problems I: One-Dimensional Convection-Diffusion. Computing 66, 163–178 (2001). https://doi.org/10.1007/s006070170033

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  • DOI: https://doi.org/10.1007/s006070170033

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