Hartmann, Ralf and Lukacova-Medvidova, M. and Prill, F. (2009) Efficient Preconditioning for the Discontinuous Galerkin Finite Element Method by Low-Order Elements. Applied Numerical Mathematics, 59 (8), pp. 1737-1753. Elsevier. doi: 10.1016/j.apnum.2009.01.002. ISSN 0168-9274.
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Abstract
We derive and analyze a block diagonal preconditioner for the linear problems arising from a discontinuous Galerkin finite element discretization. The method can be applied to second-order self-adjoint elliptic boundary value problems and exploits the natural decomposition of the discrete function space into a global low-order subsystem and components of higher polynomial degree. Similar to results for the p-version of the conforming FEM, we prove for the interior penalty discontinuous Galerkin discretization that the condition number of the preconditioned system grows as p<sup>2</sup> (log p + 1)<sup>2</sup>, where p is the polynomial degree of the discrete function space. Numerical experiments demonstrate the performance of the method.
Item URL in elib: | https://elib.dlr.de/63155/ | ||||||||||||||||
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Document Type: | Article | ||||||||||||||||
Title: | Efficient Preconditioning for the Discontinuous Galerkin Finite Element Method by Low-Order Elements | ||||||||||||||||
Authors: |
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Date: | August 2009 | ||||||||||||||||
Journal or Publication Title: | Applied Numerical Mathematics | ||||||||||||||||
Refereed publication: | Yes | ||||||||||||||||
Open Access: | No | ||||||||||||||||
Gold Open Access: | No | ||||||||||||||||
In SCOPUS: | Yes | ||||||||||||||||
In ISI Web of Science: | Yes | ||||||||||||||||
Volume: | 59 | ||||||||||||||||
DOI: | 10.1016/j.apnum.2009.01.002 | ||||||||||||||||
Page Range: | pp. 1737-1753 | ||||||||||||||||
Publisher: | Elsevier | ||||||||||||||||
ISSN: | 0168-9274 | ||||||||||||||||
Status: | Published | ||||||||||||||||
Keywords: | Discontinuous Galerkin method, block diagonal preconditioning, static condensation, advection-diffusion equation | ||||||||||||||||
HGF - Research field: | Aeronautics, Space and Transport | ||||||||||||||||
HGF - Program: | Aeronautics | ||||||||||||||||
HGF - Program Themes: | Aircraft Research (old) | ||||||||||||||||
DLR - Research area: | Aeronautics | ||||||||||||||||
DLR - Program: | L AR - Aircraft Research | ||||||||||||||||
DLR - Research theme (Project): | L - Concepts & Integration (old) | ||||||||||||||||
Location: | Braunschweig | ||||||||||||||||
Institutes and Institutions: | Institute of Aerodynamics and Flow Technology > CASE | ||||||||||||||||
Deposited By: | Hartmann, Dr.rer.nat. Ralf | ||||||||||||||||
Deposited On: | 12 Feb 2010 12:54 | ||||||||||||||||
Last Modified: | 18 Oct 2021 09:58 |
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