Pointwise nonlinear scaling for reaction-diffusion equations

• Autores: Martin Weiser
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 59, Nº. 8, 2009, págs. 1858-1869
• Idioma: inglés
• DOI: 10.1016/j.apnum.2009.01.010
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• Resumen

  • 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.