Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients
dc.contributor.author | Ayuso Dios, Blanca | |
dc.contributor.author | Holst, Michael | |
dc.contributor.author | Zhu, Yunrong | |
dc.contributor.author | Zikatanov, Ludmil | |
dc.date.accessioned | 2016-01-19T14:45:10Z | |
dc.date.available | 2016-01-19T14:45:10Z | |
dc.date.issued | 2013-10-30 | |
dc.identifier.citation | Ayuso 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.issn | 0025-5718 | |
dc.identifier.issn | 1088-6842 | |
dc.identifier.doi | 10.1090/s0025-5718-2013-02760-3 | |
dc.identifier.uri | http://hdl.handle.net/10754/594284 | |
dc.description.abstract | We 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.publisher | American Mathematical Society (AMS) | |
dc.subject | Crouzeix-Raviart finite elements | |
dc.subject | Discontinuous Galerkin methods | |
dc.subject | Multilevel preconditioner | |
dc.subject | Space decomposition | |
dc.title | Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients | |
dc.type | Article | |
dc.contributor.department | Applied Mathematics and Computational Science Program | |
dc.contributor.department | Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ) | |
dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | |
dc.identifier.journal | Mathematics of Computation | |
dc.contributor.institution | Centre de Recerca Matematica, Campus de Bellaterra, Bellaterra, 08193, Spain | |
dc.contributor.institution | Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, United States | |
dc.contributor.institution | Department of Mathematics, Idaho State University, Pocatello, ID 83209-8085, United States | |
dc.contributor.institution | Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States | |
kaust.person | Ayuso Dios, Blanca |
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