Publisher DOI: 10.1093/imanum/drw018
Title: Auxiliary space preconditioners for SIP-DG discretizations of H(curl)-elliptic problems with discontinuous coefficients
Language: English
Authors: Ayuso De Dios, Blanca 
Hiptmair, Ralf 
Pagliantini, Cecilia 
Keywords: auxiliary space preconditioning; discontinuous coefficients; discontinuous Galerkin methods; H(curlω)-elliptic problems
Issue Date: 2-Jun-2016
Publisher: Oxford Univ. Press
Source: IMA Journal of Numerical Analysis 2 (37): 646-686 (2017)
Abstract (english): 
We propose a family of preconditioners for linear systems of equations arising from a piecewise polynomial symmetric interior penalty discontinuous Galerkin discretization of H(curl,ω)-elliptic boundary value problems on conforming meshes. The design and analysis of the proposed preconditioners rely on the auxiliary space method (ASM) employing an auxiliary space of H(curl,ω)-conforming finite element functions together with a relaxation technique (local smoothing). On simplicial meshes, the proposed preconditioner enjoys asymptotic optimality with respect to mesh refinement. It is also robust with respect to jumps in the coefficients ? and b in the second-and zeroth-order parts of the operator, respectively, except when the problem changes from curl-dominated to reaction-dominated and vice versa. On quadrilateral/hexahedral meshes some of the proposed ASM solvers may fail, since the related H(curl,ω)-conforming finite element space does not provide a spectrally accurate discretization. Extensive numerical experiments are included to verify the theory and assess the performance of the preconditioners.
ISSN: 1464-3642
Journal: IMA journal of numerical analysis 
Institute: Mathematik E-10 
Document Type: Article
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