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dc.contributor.authorAyuso Dios, Blanca
dc.contributor.authorHolst, Michael
dc.contributor.authorZhu, Yunrong
dc.contributor.authorZikatanov, Ludmil
dc.date.accessioned2016-01-19T14:45:10Z
dc.date.available2016-01-19T14:45:10Z
dc.date.issued2013-10-30
dc.identifier.citationAyuso de Dios B, Holst M, Zhu Y, Zikatanov L (2013) Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients. Math Comp 83: 1083–1120. Available: http://dx.doi.org/10.1090/s0025-5718-2013-02760-3.
dc.identifier.issn0025-5718
dc.identifier.issn1088-6842
dc.identifier.doi10.1090/s0025-5718-2013-02760-3
dc.identifier.urihttp://hdl.handle.net/10754/594284
dc.description.abstractWe introduce and analyze two-level and multilevel preconditioners for a family of Interior Penalty (IP) discontinuous Galerkin (DG) discretizations of second order elliptic problems with large jumps in the diffusion coefficient. Our approach to IPDG-type methods is based on a splitting of the DG space into two components that are orthogonal in the energy inner product naturally induced by the methods. As a result, the methods and their analysis depend in a crucial way on the diffusion coefficient of the problem. The analysis of the proposed preconditioners is presented for both symmetric and non-symmetric IP schemes; dealing simultaneously with the jump in the diffusion coefficient and the non-nested character of the relevant discrete spaces presents additional difficulties in the analysis, which precludes a simple extension of existing results. However, we are able to establish robustness (with respect to the diffusion coefficient) and near-optimality (up to a logarithmic term depending on the mesh size) for both two-level and BPX-type preconditioners, by using a more refined Conjugate Gradient theory. Useful by-products of the analysis are the supporting results on the construction and analysis of simple, efficient and robust two-level and multilevel preconditioners for non-conforming Crouzeix-Raviart discretizations of elliptic problems with jump coefficients. Following the analysis, we present a sequence of detailed numerical results which verify the theory and illustrate the performance of the methods. © 2013 American Mathematical Society.
dc.publisherAmerican Mathematical Society (AMS)
dc.subjectCrouzeix-Raviart finite elements
dc.subjectDiscontinuous Galerkin methods
dc.subjectMultilevel preconditioner
dc.subjectSpace decomposition
dc.titleMultilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalMathematics of Computation
dc.contributor.institutionCentre de Recerca Matematica, Campus de Bellaterra, Bellaterra, 08193, Spain
dc.contributor.institutionDepartment of Mathematics, University of California, San Diego, La Jolla, CA 92093, United States
dc.contributor.institutionDepartment of Mathematics, Idaho State University, Pocatello, ID 83209-8085, United States
dc.contributor.institutionDepartment of Mathematics, Pennsylvania State University, University Park, PA 16802, United States
kaust.personAyuso Dios, Blanca


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