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Full Finite Element Scheme for Reaction-Diffusion Systems on Embedded Curved Surfaces in

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  • D. Assaely León-Velasco
  • Guillermo Chacón-Acosta

Abstract

The purpose of this article is to study numerically the Turing diffusion-driven instability mechanism for pattern formation on curved surfaces embedded in , specifically the surface of the sphere and the torus with some well-known kinetics. To do this, we use Euler’s backward scheme for discretizing time. For spatial discretization, we parameterize the surface of the torus in the standard way, while for the sphere, we do not use any parameterization to avoid singularities. For both surfaces, we use finite element approximations with first-order polynomials.

Suggested Citation

  • D. Assaely León-Velasco & Guillermo Chacón-Acosta, 2021. "Full Finite Element Scheme for Reaction-Diffusion Systems on Embedded Curved Surfaces in," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-16, April.
    • Handle: RePEc:hin:jnlamp:8898484
    DOI: 10.1155/2021/8898484
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