{"paper":{"title":"Multilevel Preconditioners for Discontinuous Galerkin Approximations of Elliptic Problems with Jump Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Blanca Ayuso De Dios, Ludmil Zikatanov, Michael Holst, Yunrong Zhu","submitted_at":"2010-12-06T19:11:49Z","abstract_excerpt":"We introduce and analyze two-level and multi-level 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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1287","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}