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.
| 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 |
| ZIB-Reportnumber: | 07-45 |
| Published in: | Appeared in: Applied Numerical Mathematics 59 (2009), pp. 1858-1869. DOI information: 10.1016/j.apnum.2009.01.010 |

