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dc.contributor.authorChu, Van Tiepen_US
dc.contributor.authorHoang, Viet Haen_US
dc.contributor.authorLim, Roktaeken_US
dc.identifier.citationChu, V. T., Hoang, V. H. & Lim, R. (2021). Sparse tensor product high dimensional finite elements for two-scale mixed problems. Computers and Mathematics With Applications, 85, 42-56.
dc.description.abstractWe develop the essentially optimal sparse tensor product finite element method for solving two-scale mixed problems in both the primal and dual forms. We study the two-scale homogenized mixed problems which are obtained in the limit where the microscopic scale tends to zero. These limiting problems are posed in a high dimensional tensorized product domain. Using sparse tensor product finite elements, we solve these problems with essentially optimal complexity to obtain an approximation for the solution within a prescribed accuracy. This is achieved when the solutions of the high dimensional two-scale homogenized mixed problems possess sufficient regularity with respect to both the slow and the fast variable at the same time. We show that this regularity requirement holds when the two-scale coefficient and the forcing satisfy mild smoothness conditions. From the finite element solutions for the two-scale homogenized mixed problems, we construct numerical correctors for the solutions of the original two-scale mixed problems. We prove an error estimate for these correctors in terms of both the homogenization error and the finite element error. Numerical examples confirm the theoretical results.en_US
dc.description.sponsorshipAgency for Science, Technology and Research (A*STAR)en_US
dc.description.sponsorshipMinistry of Education (MOE)en_US
dc.relation.ispartofComputers and Mathematics with Applicationsen_US
dc.rights© 2021 Elsevier Ltd. All rights reserved.en_US
dc.titleSparse tensor product high dimensional finite elements for two-scale mixed problemsen_US
dc.typeJournal Articleen
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.subject.keywordsOptimal Complexityen_US
dc.subject.keywordsNumerical Correctoren_US
dc.description.acknowledgementViet Ha Hoang and Roktaek Lim are supported by the Singapore A*Star SERC grant 122-PSF-0007. Van Tiep Chu and Viet Ha Hoang are supported by the Singapore MOE Tier 2 grant MOE2017-T2-2-144.en_US
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