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dc.contributor.authorRussell, Stephen
dc.contributor.authorMadden, Niall
dc.identifier.citationRussell, Stephen; Madden, Niall (2017). An introduction to the analysis and implementation of sparse grid finite element methods. Computational Methods in Applied Mathematics 17 (2), 299-322
dc.description.abstractOur goal is to present an elementary approach to the analysis and programming of sparse grid finite element methods. This family of schemes can compute accurate solutions to partial differential equations, but using far fewer degrees of freedom than their classical counterparts. After a brief discussion of the classical Galerkin finite element method with bilinear elements, we give a short analysis of what is probably the simplest sparse grid method: the two-scale technique of Lin et al. [14]. We then demonstrate how to extend this to a multiscale sparse grid method which, up to choice of basis, is equivalent to the hierarchical approach, as described by, e.g., Bungartz and Griebel [4]. However, by presenting it as an extension of the two-scale method, we can give an elementary treatment of its analysis and implementation. For each method considered, we provide MATLAB code, and a comparison of accuracy and computational costs.
dc.publisherWalter de Gruyter GmbH
dc.relation.ispartofComputational Methods in Applied Mathematics
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Ireland
dc.subjectfinite element
dc.subjectsparse grids
dc.subjecttwo-scale discretisation
dc.subjectmultiscale discretisation
dc.subjectcombination technique
dc.titleAn introduction to the analysis and implementation of sparse grid finite element methods

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