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A multigrid finite element method for reaction-diffusion systems on surfaces

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Computing and Visualization in Science

Abstract

We develop a multigrid finite element approach to solve PDE’s on surfaces. The multigrid approach involves the same weights for restriction and prolongation as in the case of planar domains. Combined with the concept of parametric finite elements the approach thus allows to reuse code initially developed to solve problems on planar domains to solve the corresponding problem on surfaces. The method is tested on a non-linear reaction-diffusion system on stationary and evolving surfaces, with the normal velocity of the evolving surface depending on the reaction-diffusion system. As a reference model the Schnakenberg system is used, offering non-linearity and algebraic simplicity on one hand, and quantitative reference data on the other hand.

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Authors and Affiliations

  1. Institut für Wissenschaftliches Rechnen, Dresden, Germany

    Christoph Landsberg & Axel Voigt

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  1. Christoph Landsberg
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  2. Axel Voigt
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Correspondence to Christoph Landsberg.

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Landsberg, C., Voigt, A. A multigrid finite element method for reaction-diffusion systems on surfaces. Comput. Visual Sci. 13, 177–185 (2010). https://doi.org/10.1007/s00791-010-0136-2

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  • DOI: https://doi.org/10.1007/s00791-010-0136-2

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