Resumen de Pointwise nonlinear scaling for reaction-diffusion equations

Martin Weiser

• 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.