dc.contributor.author Russell, Stephen dc.contributor.author Madden, Niall dc.date.accessioned 2018-09-20T16:23:27Z dc.date.available 2018-09-20T16:23:27Z dc.date.issued 2017-01-01 dc.identifier.citation Russell, 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.identifier.issn 1609-4840,1609-9389 dc.identifier.uri http://hdl.handle.net/10379/13735 dc.description.abstract Our 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.publisher Walter de Gruyter GmbH dc.relation.ispartof Computational Methods in Applied Mathematics dc.rights Attribution-NonCommercial-NoDerivs 3.0 Ireland dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/3.0/ie/ dc.subject finite element dc.subject sparse grids dc.subject two-scale discretisation dc.subject multiscale discretisation dc.subject matlab dc.subject combination technique dc.title An introduction to the analysis and implementation of sparse grid finite element methods dc.type Article dc.identifier.doi 10.1515/cmam-2016-0042 dc.local.publishedsource http://arxiv.org/pdf/1511.07193 nui.item.downloads 0
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