Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain

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dc.contributor.authorWang, W.
dc.contributor.authorRoberts, A.
dc.contributor.departmentFaculty of Engineering, Computer & Mathematical Sciences
dc.date.issued2011
dc.description.abstractDynamical 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.
dc.description.statementofresponsibilityWei Wang, Anthony Roberts
dc.identifier.citationDiscrete and Continuous Dynamical Systems Series A, 2011; 31(1):253-273
dc.identifier.doi10.3934/dcds.2011.31.253
dc.identifier.issn1078-0947
dc.identifier.issn1553-5231
dc.identifier.orcidRoberts, A. [0000-0001-8930-1552]
dc.identifier.urihttp://hdl.handle.net/2440/80419
dc.language.isoen
dc.publisherSouthwest Missouri State Univ
dc.relation.granthttp://purl.org/au-research/grants/arc/DP0774311
dc.relation.granthttp://purl.org/au-research/grants/arc/DP0988738
dc.relation.granthttp://purl.org/au-research/grants/arc/DP0988738
dc.relation.granthttp://purl.org/au-research/grants/arc/DP0774311
dc.rightsCopyright status unknown
dc.source.urihttps://doi.org/10.3934/dcds.2011.31.253
dc.subjectStochastic reaction-diffusion equation
dc.subjectaveraging
dc.subjectoverlapping finite elements
dc.subjectinterelement coupling
dc.titleMacroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain
dc.typeJournal article
pubs.publication-statusPublished

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