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hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains

Antonietti, Paola F.; Giani, Stefano; Houston, Paul

Authors

Paola F. Antonietti paola.antonietti@polimi.it

Stefano Giani stefano.giani@nottingham.ac.uk

PAUL HOUSTON paul.houston@nottingham.ac.uk
Professor of Computational and Applied Maths



Abstract

In this paper we introduce the hp-version discontinuous Galerkin composite finite element method for the discretization of second-order elliptic partial differential equations. This class of methods allows for the approximation of problems posed on computational domains which may contain a huge number of local geometrical features, or micro-structures. While standard numerical methods can be devised for such problems, the computational effort may be extremely high, as the minimal number of elements needed to represent the underlying domain can be very large. In contrast, the minimal dimension of the underlying composite finite element space is independent of the number of geometric features. The key idea in the construction of this latter class of methods is that the computational domain Ω is no longer resolved by the mesh; instead, the finite element basis (or shape) functions are adapted to the geometric details present in Ω. In this article, we extend these ideas to the discontinuous Galerkin setting, based on employing the hp-version of the finite element method. Numerical experiments highlighting the practical application of the proposed numerical scheme will be presented.

Citation

Antonietti, P. F., Giani, S., & Houston, P. (2013). hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains. SIAM Journal on Scientific Computing, 35(3), https://doi.org/10.1137/120877246

Journal Article Type Article
Acceptance Date Feb 20, 2013
Publication Date May 30, 2013
Deposit Date May 15, 2012
Publicly Available Date May 30, 2013
Journal SIAM Journal on Scientific Computing
Print ISSN 1064-8275
Electronic ISSN 1064-8275
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 35
Issue 3
Article Number A1417-A1439
DOI https://doi.org/10.1137/120877246
Public URL http://eprints.nottingham.ac.uk/id/eprint/1618
Publisher URL https://epubs.siam.org/doi/10.1137/120877246
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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