Name
Title | ||
|---|---|---|
Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients. |
Abstract | ||
|---|---|---|
We introduce and analyzetwo-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. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1090/S0025-5718-2013-02760-3 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
Multilevel preconditioner,discontinuous Galerkin methods,Crouzeix-Raviart finite elements,space decomposition | Discontinuous Galerkin method,Mathematical optimization,Mathematical analysis,Galerkin method,Approximations of π,Robustness (computer science),Space decomposition,Jump,Hinge,Mathematics,Preprint | Journal |
Volume | Issue | ISSN |
83 | 287 | 0025-5718 |
Citations | PageRank | References |
6 | 0.55 | 34 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Blanca Ayuso De Dios | 1 | 33 | 2.85 |
| Michael Holst | 2 | 60 | 7.84 |
| Yunrong Zhu | 3 | 28 | 3.86 |
| Ludmil Zikatanov | 4 | 189 | 25.89 |