SUPG-based stabilization using a separated representations approach
| Autor: | Antonio Huerta, Francisco Chinesta, L. Debeugny, Elías Cueto, D. González, Pedro Díez |
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| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
| Předmět: |
Engineering
Civil Finite element method Generalization Separation of variables Petrov–Galerkin method Elements finits Mètode dels Engineering Multidisciplinary Context (language use) Numerical methods and algorithms General Materials Science Engineering Ocean Representation (mathematics) Finite set Engineering Aerospace Engineering Biomedical Mathematics Anàlisi numèrica Sequence Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics [Àrees temàtiques de la UPC] Mathematical analysis Differential equations Partial Equacions diferencials parcials Computer Science Software Engineering Engineering Marine Engineering Manufacturing Engineering Mechanical Engineering Industrial Convection–diffusion equation |
| Zdroj: | Recercat. Dipósit de la Recerca de Catalunya instname UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Scipedia Open Access Scipedia SL |
| Popis: | We have developed a new method for the construction of Streamline Upwind Petrov Galerkin (SUPG) stabilization techniques for the resolution of convection-diffusion equations based on the use of separated representations inside the Proper Generalized Decompositions (PGD) framework. The use of SUPG schemes produces a consistent stabilization adding a parameter to all the terms of the equation (not only the convective one). SUPG obtains an exact solution for problems in 1D, nevertheless, a generalization does not exist for elements of high order or for any system of convection-diffusion equations. We introduce in this paper a method that achieves stabilization in the context of Proper Generalzied Decomposition (PGD). This class of approximations use a representation of the solution by means of the sum of a finite number of terms of separable functions. Thus it is possible to use the technique of separation of variables in the context of problems of convection-diffusion that will lead to a sequence of problems in 1D where the parameter of stabilization is well known. |
| Databáze: | OpenAIRE |
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