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Adaptive finite element for semi-linear convection–diffusion problems

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Abstract

In this article a strategy of adaptive finite element for semi-linear problems, based on minimizing a residual-type estimator, is reported. We get an a posteriori error estimate which is asymptotically exact when the mesh size h tends to zero. By considering a model problem, the quality of this estimator is checked. It is numerically shown that without constraint on the mesh size h, the efficiency of the a posteriori error estimate can fail dramatically. This phenomenon is analysed and an algorithm which equidistributes the local estimators under the constraint h ⩽ h max is proposed. This algorithm allows to improve the computed solution for semi-linear convection–diffusion problems, and can be used for stabilizing the Lagrange finite element method for linear convection–diffusion problems.

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Authors and Affiliations

  1. Department of Mathematics, Swiss Federal Institute of Technology, CH-1015, Lausanne, Switzerland

    L. Pouly

  2. Mathematical Modelling and Scientific Computing Laboratory, UMR CNRS 5585, National Institute of Applied Sciences in Lyon, 20 av. Einstein, F-69621, Villeurbanne Cedex, France

    J. Pousin

Authors
  1. L. Pouly
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  2. J. Pousin
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Pouly, L., Pousin, J. Adaptive finite element for semi-linear convection–diffusion problems. Advances in Computational Mathematics 7, 235–259 (1997). https://doi.org/10.1023/A:1018946919497

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