Pointwise Nonlinear Scaling for Reaction-Diffusion-Equations

Please always quote using this URN: urn:nbn:de:0297-zib-10493
  • Parabolic reaction-diffusion systems may develop sharp moving reaction fronts which pose a challenge even for adaptive finite element methods. We propose a method to transform the equation into an equivalent form that usually exhibits solutions which are easier to discretize, giving higher accuracy for a given number of degrees of freedom. The transformation is realized as an efficiently computable pointwise nonlinear scaling that is optimized for prototypical planar travelling wave solutions of the underlying reaction-diffusion equation. The gain in either performance or accuracy is demonstrated on different numerical examples.

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Metadaten
Author:Martin WeiserORCiD
Document Type:ZIB-Report
Tag:discretization error; nonlinear scaling; reaction-diffusion equations; travelling waves
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M50 Mesh generation and refinement
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Date of first Publication:2007/12/21
Series (Serial Number):ZIB-Report (07-45)
ISSN:1438-0064
Published in:Appeared in: Applied Numerical Mathematics 59 (2009), pp. 1858-1869. DOI information: 10.1016/j.apnum.2009.01.010