Adaptive discontinuous Galerkin methods on polytopic meshes
In this article we consider the application of discontinuous Galerkin finite element methods, defined on agglomerated meshes consisting of general polytopic elements, to the numerical approximation of partial differential equation problems posed on complicated geometries. Here, we assume that the un...
| Main Authors: | , |
|---|---|
| Format: | Conference or Workshop Item |
| Published: |
2016
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/32578/ |
| _version_ | 1848794440320155648 |
|---|---|
| author | Collis, Joe Houston, Paul |
| author_facet | Collis, Joe Houston, Paul |
| author_sort | Collis, Joe |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this article we consider the application of discontinuous Galerkin finite element methods, defined on agglomerated meshes consisting of general polytopic elements, to the numerical approximation of partial differential equation problems posed on complicated geometries. Here, we assume that the underlying computational domain may be accurately represented by a geometry-conforming fine mesh; the resulting coarse mesh is then constructed based on employing standard graph partitioning algorithms. To improve the accuracy of the computed numerical approximation, we consider the development of goal-oriented adaptation techniques within an automatic mesh refinement strategy. In this setting, elements marked for refinement are subdivided by locally constructing finer agglomerates; should further resolution of the underlying fine mesh T_f be required, then adaptive refinement of T_f will also be undertaken. As an example of the application of these techniques, we consider the numerical approximation of the linear elasticity equations for a homogeneous isotropic material. In particular, the performance of the proposed adaptive refinement algorithm is studied for the computation of the (scaled) effective Young's modulus of a section of trabecular bone. |
| first_indexed | 2025-11-14T19:16:13Z |
| format | Conference or Workshop Item |
| id | nottingham-32578 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:16:13Z |
| publishDate | 2016 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-325782020-05-04T18:05:43Z https://eprints.nottingham.ac.uk/32578/ Adaptive discontinuous Galerkin methods on polytopic meshes Collis, Joe Houston, Paul In this article we consider the application of discontinuous Galerkin finite element methods, defined on agglomerated meshes consisting of general polytopic elements, to the numerical approximation of partial differential equation problems posed on complicated geometries. Here, we assume that the underlying computational domain may be accurately represented by a geometry-conforming fine mesh; the resulting coarse mesh is then constructed based on employing standard graph partitioning algorithms. To improve the accuracy of the computed numerical approximation, we consider the development of goal-oriented adaptation techniques within an automatic mesh refinement strategy. In this setting, elements marked for refinement are subdivided by locally constructing finer agglomerates; should further resolution of the underlying fine mesh T_f be required, then adaptive refinement of T_f will also be undertaken. As an example of the application of these techniques, we consider the numerical approximation of the linear elasticity equations for a homogeneous isotropic material. In particular, the performance of the proposed adaptive refinement algorithm is studied for the computation of the (scaled) effective Young's modulus of a section of trabecular bone. 2016-08-25 Conference or Workshop Item NonPeerReviewed Collis, Joe and Houston, Paul (2016) Adaptive discontinuous Galerkin methods on polytopic meshes. In: X-DMS eXtended Discretization Methods, 9-11 Sept 2015, Ferrara, Italy. discontinuous Galerkin methods; polytopic elements; hp–finite element methods http://link.springer.com/chapter/10.1007%2F978-3-319-41246-7_9 |
| spellingShingle | discontinuous Galerkin methods; polytopic elements; hp–finite element methods Collis, Joe Houston, Paul Adaptive discontinuous Galerkin methods on polytopic meshes |
| title | Adaptive discontinuous Galerkin methods on polytopic meshes |
| title_full | Adaptive discontinuous Galerkin methods on polytopic meshes |
| title_fullStr | Adaptive discontinuous Galerkin methods on polytopic meshes |
| title_full_unstemmed | Adaptive discontinuous Galerkin methods on polytopic meshes |
| title_short | Adaptive discontinuous Galerkin methods on polytopic meshes |
| title_sort | adaptive discontinuous galerkin methods on polytopic meshes |
| topic | discontinuous Galerkin methods; polytopic elements; hp–finite element methods |
| url | https://eprints.nottingham.ac.uk/32578/ https://eprints.nottingham.ac.uk/32578/ |