Boletín SEMA, No 47 (2009)

Tamaño de la letra:  Pequeña  Mediana  Grande

MULTIRESOLUTION SIMULATION OF REACTION-DIFFUSION SYSTEMS WITH STRONG DEGENERACY

R. Bürger, R. Ruiz-Baier

Resumen


A fully space-adaptive multiresolution method is applied to an explicit
finite volume scheme for solving a strongly degenerate reaction-diffusion
system. Since a closed mathematical theory is lacking, insight into
the behaviour of these systems, in particular into the spatial patterns
their solutions may exhibit, can be currently obtained by numerical
experimentation only. It is demonstrated that the present space-
adaptive scheme is an appropriate tool for this purpose. In particular,
the multiresolution method and the classical finite volume scheme are
compared and the numerical results show that this strategy provides
substantial savings in terms of data storage and computational effort,
while giving an accurate approximation to the sought quantities.


Key words: Adaptive multiresolution schemes, Degenerate diffusion, Pattern-
formation, Turing instability.


AMS sub ject classifications:
65M06, 35K55.


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