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Analysis of a FEM for a coupled system of singularly perturbed reaction–diffusion equations

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Abstract

We consider a system of ℓ ≥ 2 one-dimensional singularly perturbed reaction–diffusion equations coupled at the zero-order term. The second derivative of each equation is multiplied by a distinct small parameter. We present a convergence theory for conforming linear finite elements on arbitrary meshes. As a result convergence independently of the perturbation parameters on a wide class of layer-adapted meshes is established.

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  1. Institut für Numerische Mathematik, Technische Universität Dresden, 01062, Dresden, Germany

    Torsten Linß

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  1. Torsten Linß
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Correspondence to Torsten Linß.

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Linß, T. Analysis of a FEM for a coupled system of singularly perturbed reaction–diffusion equations. Numer Algor 50, 283–291 (2009). https://doi.org/10.1007/s11075-008-9228-1

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  • DOI: https://doi.org/10.1007/s11075-008-9228-1

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