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Sufficient conditions for uniform convergence on layer-adapted meshes for one-dimensional reaction–diffusion problems

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Abstract

We study convergence properties of a finite element method with lumping for the solution of linear one-dimensional reaction–diffusion problems on arbitrary meshes. We derive conditions that are sufficient for convergence in the L∞ norm, uniformly in the diffusion parameter, of the method. These conditions are easy to check and enable one to immediately deduce the rate of convergence. The key ingredients of our analysis are sharp estimates for the discrete Green function associated with the discretization.

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Authors and Affiliations

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

    Torsten Linß

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  1. Torsten Linß
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Correspondence to Torsten Linß.

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65L10, 65L12, 65L15

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Linß, T. Sufficient conditions for uniform convergence on layer-adapted meshes for one-dimensional reaction–diffusion problems. Numer Algor 40, 23–32 (2005). https://doi.org/10.1007/s11075-005-2265-0

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  • DOI: https://doi.org/10.1007/s11075-005-2265-0

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