Hartmann, Ralf and Lukacova-Medvidova, M. and Prill, F. (2010) Efficient Preconditioning for the Discontinuous Galerkin Finite Element Method by Low-Order Elements. Applied Numerical Mathematics, 59 (8), pp. 1737-1753. Elsevier. 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: | 12 February 2010 | ||||||||||||
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 | ||||||||||||
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: | 01 Dec 2018 19:47 |
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