Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model
We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is well-posed (stable) with a thickness-dependent constant in a norm enc...
| Main Authors: | , , |
|---|---|
| Format: | Journal Article |
| Published: |
Pergamon Press
2014
|
| Online Access: | http://hdl.handle.net/20.500.11937/51348 |
| _version_ | 1848758675341049856 |
|---|---|
| author | Calo, Victor Collier, N. Niemi, A. |
| author_facet | Calo, Victor Collier, N. Niemi, A. |
| author_sort | Calo, Victor |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is well-posed (stable) with a thickness-dependent constant in a norm encompassing the L2-norms of the bending moment, the shear force, the transverse deflection and the rotation vector. We then construct a numerical solution scheme based on quadrilateral scalar and vector finite elements of degree p. We show that for affine meshes the discretization inherits the stability of the continuous formulation provided that the optimal test functions are approximated by polynomials of degree p+3. We prove a theoretical error estimate in terms of the mesh size h and polynomial degree p and demonstrate numerical convergence on affine as well as non-affine mesh sequences. © 2013 Elsevier Ltd. All rights reserved. |
| first_indexed | 2025-11-14T09:47:45Z |
| format | Journal Article |
| id | curtin-20.500.11937-51348 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:47:45Z |
| publishDate | 2014 |
| publisher | Pergamon Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-513482018-03-29T09:08:25Z Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model Calo, Victor Collier, N. Niemi, A. We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is well-posed (stable) with a thickness-dependent constant in a norm encompassing the L2-norms of the bending moment, the shear force, the transverse deflection and the rotation vector. We then construct a numerical solution scheme based on quadrilateral scalar and vector finite elements of degree p. We show that for affine meshes the discretization inherits the stability of the continuous formulation provided that the optimal test functions are approximated by polynomials of degree p+3. We prove a theoretical error estimate in terms of the mesh size h and polynomial degree p and demonstrate numerical convergence on affine as well as non-affine mesh sequences. © 2013 Elsevier Ltd. All rights reserved. 2014 Journal Article http://hdl.handle.net/20.500.11937/51348 10.1016/j.camwa.2013.07.012 Pergamon Press restricted |
| spellingShingle | Calo, Victor Collier, N. Niemi, A. Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model |
| title | Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model |
| title_full | Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model |
| title_fullStr | Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model |
| title_full_unstemmed | Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model |
| title_short | Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model |
| title_sort | analysis of the discontinuous petrov-galerkin method with optimal test functions for the reissner-mindlin plate bending model |
| url | http://hdl.handle.net/20.500.11937/51348 |