hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains
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 numb...
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| Format: | Article |
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Society for Industrial and Applied Mathematics
2013
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| Online Access: | https://eprints.nottingham.ac.uk/1618/ |
| _version_ | 1848790639713452032 |
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| author | Antonietti, Paola F. Giani, Stefano Houston, Paul |
| author_facet | Antonietti, Paola F. Giani, Stefano Houston, Paul |
| author_sort | Antonietti, Paola F. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:15:49Z |
| format | Article |
| id | nottingham-1618 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:15:49Z |
| publishDate | 2013 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-16182020-05-04T16:36:42Z https://eprints.nottingham.ac.uk/1618/ hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains Antonietti, Paola F. Giani, Stefano Houston, Paul 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. Society for Industrial and Applied Mathematics 2013-05-30 Article PeerReviewed Antonietti, Paola F., Giani, Stefano and Houston, Paul (2013) hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains. SIAM Journal on Scientific Computing, 35 (3). A1417-A1439. ISSN 1064-8275 https://epubs.siam.org/doi/10.1137/120877246 doi:10.1137/120877246 doi:10.1137/120877246 |
| spellingShingle | Antonietti, Paola F. Giani, Stefano Houston, Paul hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains |
| title | hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains |
| title_full | hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains |
| title_fullStr | hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains |
| title_full_unstemmed | hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains |
| title_short | hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains |
| title_sort | hp-version composite discontinuous galerkin methods for elliptic problems on complicated domains |
| url | https://eprints.nottingham.ac.uk/1618/ https://eprints.nottingham.ac.uk/1618/ https://eprints.nottingham.ac.uk/1618/ |