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Type: Journal article
Title: Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations
Author: Bunder, J.
Roberts, A.
Citation: Applied Mathematics and Computation, 2017; 304:164-179
Publisher: Elsevier
Issue Date: 2017
ISSN: 0096-3003
Statement of
J.E. Bunder, A.J. Roberts
Abstract: Coarse grained, macroscale, spatial discretisations of nonlinear nonautonomous partial dif- ferential/difference equations are given novel support by centre manifold theory. Dividing the physical domain into overlapping macroscale elements empowers the approach to re- solve significant subgrid microscale structures and interactions between neighbouring ele- ments. The crucial aspect of this approach is that centre manifold theory organises the res- olution of the detailed subgrid microscale structure interacting via the nonlinear dynamics within and between neighbouring elements. The techniques and theory developed here may be applied to soundly discretise on a macroscale many dissipative nonautonomous partial differential/difference equations, such as the forced Burgers’ equation, adopted here as an illustrative example.
Keywords: Nonlinear nonautonomous PDEs; Spatial discretisation; Nonautonomous slow manifold; Multiscale modelling; Closure; Coarse graining
Rights: © 2017 Elsevier Inc. All rights reserved.
DOI: 10.1016/j.amc.2017.01.056
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