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

Giani, Stefano; Houston, Paul

Authors

Stefano Giani stefano.giani@durham.ac.uk

Paul Houston Paul.Houston@nottingham.ac.uk



Abstract

In this paper we develop the a posteriori error estimation of hp-version discontinuous Galerkin composite finite element methods 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. Computable bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. Numerical experiments highlighting the practical application of the proposed estimators within an automatic hp-adaptive refinement procedure will be presented.

Journal Article Type Article
Publication Date Jul 1, 2014
Journal Numerical Methods for Partial Differential Equations
Print ISSN 0749-159X
Electronic ISSN 0749-159X
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 30
Issue 4
APA6 Citation Giani, S., & Houston, P. (2014). hp-adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. Numerical Methods for Partial Differential Equations, 30(4), doi:10.1002/num.21872
DOI https://doi.org/10.1002/num.21872
Keywords composite finite element methods, discontinuous Galerkin methods, a posteriori error estimation, hp–adaptivity
Publisher URL http://onlinelibrary.wiley.com/doi/10.1002/num.21872/abstract
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information This is the peer reviewed version of the following article: Giani, S. and Houston, P. (2014), hp–Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. Numerical Methods Partial Differential Equations, 30: 1342–1367, which has been published in final form at doi: 10.1002/num.21872 This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

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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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