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

Giani, Stefano; Houston, Paul

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.

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), https://doi.org/10.1002/num.21872

• Journal Article Type: Article
• Publication Date: Jul 1, 2014
• Deposit Date: Aug 26, 2015
• Publicly Available Date: Aug 26, 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
• DOI: https://doi.org/10.1002/num.21872
• Keywords: composite finite element methods, discontinuous Galerkin methods, a posteriori error estimation, hp–adaptivity
• Public URL: https://nottingham-repository.worktribe.com/output/994990
• Publisher URL: http://onlinelibrary.wiley.com/doi/10.1002/num.21872/abstract
• 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.