1049
eng
reportzib
0
2007-12-21
2007-12-21
--
Pointwise Nonlinear Scaling for Reaction-Diffusion-Equations
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.
07-45
1438-0064
1078
urn:nbn:de:0297-zib-10493
Appeared in: Applied Numerical Mathematics 59 (2009), pp. 1858-1869. DOI information: 10.1016/j.apnum.2009.01.010
Martin Weiser
unknown unknown
ZIB-Report
07-45
eng
uncontrolled
reaction-diffusion equations
eng
uncontrolled
travelling waves
eng
uncontrolled
nonlinear scaling
eng
uncontrolled
discretization error
Mathematik
Mesh generation and refinement
Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Numerical Mathematics
Computational Medicine
Weiser, Martin
ZIB-Cardio
ZIB-Kaskade7
https://opus4.kobv.de/opus4-zib/files/1049/ZR_07_45.pdf