Discontinuous Galerkin Methods for the Biharmonic Problem
This work is concerned with the design and analysis of hp-version discontinuous Galerkin (DG) finite element methods for boundary-value problems involving the biharmonic operator. The first part extends the unified approach of Arnold, Brezzi, Cockburn & Marini (SIAM J. Numer. Anal. 39, 5 (2001/0...
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| author | Georgoulis, Emmanuil H. Houston, Paul |
| author_facet | Georgoulis, Emmanuil H. Houston, Paul |
| author_sort | Georgoulis, Emmanuil H. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This work is concerned with the design and analysis of hp-version discontinuous Galerkin (DG) finite element methods for boundary-value problems involving the biharmonic operator. The first part extends the unified approach of Arnold, Brezzi, Cockburn & Marini (SIAM J. Numer. Anal. 39, 5 (2001/02), 1749-1779) developed for the Poisson problem, to the design of DG methods via an appropriate choice of numerical flux functions for fourth order problems; as an example we retrieve the interior penalty DG method developed by Suli & Mozolevski (Comput. Methods Appl. Mech. Engrg. 196, 13-16 (2007), 1851-1863). The second part of this work is concerned with a new a-priori error analysis of the hp-version interior penalty DG method, when the error is measured in terms of both the energy-norm and L2-norm, as well certain linear functionals of the solution, for elemental polynomial degrees $p\ge 2$. Also, provided that the solution is piecewise analytic in an open neighbourhood of each element, exponential convergence is also proven for the p-version of the DG method. The sharpness of the theoretical developments is illustrated by numerical experiments. |
| first_indexed | 2025-11-14T18:12:58Z |
| format | Article |
| id | nottingham-671 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:12:58Z |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-6712020-05-04T20:34:36Z https://eprints.nottingham.ac.uk/671/ Discontinuous Galerkin Methods for the Biharmonic Problem Georgoulis, Emmanuil H. Houston, Paul This work is concerned with the design and analysis of hp-version discontinuous Galerkin (DG) finite element methods for boundary-value problems involving the biharmonic operator. The first part extends the unified approach of Arnold, Brezzi, Cockburn & Marini (SIAM J. Numer. Anal. 39, 5 (2001/02), 1749-1779) developed for the Poisson problem, to the design of DG methods via an appropriate choice of numerical flux functions for fourth order problems; as an example we retrieve the interior penalty DG method developed by Suli & Mozolevski (Comput. Methods Appl. Mech. Engrg. 196, 13-16 (2007), 1851-1863). The second part of this work is concerned with a new a-priori error analysis of the hp-version interior penalty DG method, when the error is measured in terms of both the energy-norm and L2-norm, as well certain linear functionals of the solution, for elemental polynomial degrees $p\ge 2$. Also, provided that the solution is piecewise analytic in an open neighbourhood of each element, exponential convergence is also proven for the p-version of the DG method. The sharpness of the theoretical developments is illustrated by numerical experiments. Article NonPeerReviewed Georgoulis, Emmanuil H. and Houston, Paul Discontinuous Galerkin Methods for the Biharmonic Problem. IMA Journal of Numerical Analysis . (Submitted) Discontinuous Galerkin Methods Biharmonic finite element methods |
| spellingShingle | Discontinuous Galerkin Methods Biharmonic finite element methods Georgoulis, Emmanuil H. Houston, Paul Discontinuous Galerkin Methods for the Biharmonic Problem |
| title | Discontinuous Galerkin Methods for the Biharmonic Problem |
| title_full | Discontinuous Galerkin Methods for the Biharmonic Problem |
| title_fullStr | Discontinuous Galerkin Methods for the Biharmonic Problem |
| title_full_unstemmed | Discontinuous Galerkin Methods for the Biharmonic Problem |
| title_short | Discontinuous Galerkin Methods for the Biharmonic Problem |
| title_sort | discontinuous galerkin methods for the biharmonic problem |
| topic | Discontinuous Galerkin Methods Biharmonic finite element methods |
| url | https://eprints.nottingham.ac.uk/671/ |