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hp–Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains

Giani, Stefano; Houston, Paul

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Authors

Paul Houston



Abstract

In this article, 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 microstructures. Although 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.

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), 1342-1367. https://doi.org/10.1002/num.21872

Journal Article Type Article
Acceptance Date Feb 17, 2014
Publication Date Jul 1, 2014
Deposit Date Sep 29, 2014
Publicly Available Date Oct 13, 2015
Journal Numerical Methods for Partial Differential Equations
Print ISSN 0749-159X
Electronic ISSN 1098-2426
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 30
Issue 4
Pages 1342-1367
DOI https://doi.org/10.1002/num.21872
Keywords Composite finite element methods, Discontinuous Galerkin methods, A posteriori error estimation, hp–adaptivity.

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Copyright Statement
This is the accepted 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 for Partial Differential Equations, 30(4): 1342-1367, which has been published in final form at http://dx.doi.org/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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