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|Title:||Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations|
|Citation:||Applied Mathematics and Computation, 2017; 304:164-179|
|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.|
|Appears in Collections:||Aurora harvest 4|
Mathematical Sciences publications
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