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https://hdl.handle.net/2440/80419
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Type: | Journal article |
Title: | Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain |
Author: | Wang, W. Roberts, A. |
Citation: | Discrete and Continuous Dynamical Systems Series A, 2011; 31(1):253-273 |
Publisher: | Southwest Missouri State Univ |
Issue Date: | 2011 |
ISSN: | 1078-0947 1553-5231 |
Department: | Faculty of Engineering, Computer & Mathematical Sciences |
Statement of Responsibility: | Wei Wang, Anthony Roberts |
Abstract: | Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class of stochastic reaction-diffusion partial differential equations with cubic nonlinearity. Dividing space into overlapping finite elements, a special coupling condition between neighbouring elements preserves the self-adjoint dynamics and controls interelement interactions. When the interelement coupling parameter is small, an averaging method and an asymptotic expansion of the slow modes show that the macroscopic discrete model will be a family of coupled stochastic ordinary differential equations which describe the evolution of the grid values. This modelling shows the importance of subgrid scale interaction between noise and spatial diffusion and provides a new rigourous approach to constructing semi-discrete approximations to stochastic reaction-diffusion partial differential equations. |
Keywords: | Stochastic reaction-diffusion equation averaging overlapping finite elements interelement coupling |
Rights: | Copyright status unknown |
DOI: | 10.3934/dcds.2011.31.253 |
Grant ID: | http://purl.org/au-research/grants/arc/DP0774311 http://purl.org/au-research/grants/arc/DP0988738 http://purl.org/au-research/grants/arc/DP0988738 http://purl.org/au-research/grants/arc/DP0774311 |
Published version: | http://dx.doi.org/10.3934/dcds.2011.31.253 |
Appears in Collections: | Aurora harvest 4 Mathematical Sciences publications |
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