Error estimation for proper generalized decomposition solutions: a dual approach
The Proper Generalized Decomposition is a well established reduced order method, used to efficiently obtain approximate solutions of multi-dimensional problems in a procedure that controls the effects of the "curse of dimensionality". The question of assessing the quality of the solutions...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/343733 |
| Acceso en línea: | https://hdl.handle.net/2117/343733 https://dx.doi.org/10.1002/nme.6452 |
| Access Level: | acceso abierto |
| Palabra clave: | Numerical analysis Equilibrium formulation Error bounds Error estimation Model reduction Proper generalized decomposition Anàlisi numèrica Classificació AMS::65 Numerical analysis::65G Error analysis and interval analysis Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics |
| Sumario: | The Proper Generalized Decomposition is a well established reduced order method, used to efficiently obtain approximate solutions of multi-dimensional problems in a procedure that controls the effects of the "curse of dimensionality". The question of assessing the quality of the solutions obtained and adapting the approximations assumed, for example the finite element meshes used, so that the best result is obtained a minimal cost, remains a relevant challenge. This paper deals with finite element solutions for solid mechanics problems, using the error obtained from a dual analysis, the difference between complementary solutions, to bound the error of the solutions and to drive an optimal adaptivity process, which obtains meshes with errors significantly lower than those obtained using a uniform refinement. |
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