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Título:
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Time-accurate solution of stabilized convection-difusion-reaction equations: I - time and space discretization
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Autor/a:
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Huerta, Antonio; Donea, J
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Otros autores:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
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Abstract:
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The paper addresses the development of time-accurate methods for solving transient convection-diffusion-reaction problems using finite elements. Multi-stage time-stepping schemes of high accuracy are used. They are first combined with a Galerkin formulation to briefly recall the time-space discretization. Then spatial stabilization techniques are combined with high-order time-stepping schemes. Moreover, a least-squares formulation is also developed for these high-order time schemes combined with C0 finite elements (in spite of the diffusion operator and without reducing the strong form into a system of first-order differential equations). The weak forms induced by the SUPG, GLS, SGS and least-squares formulations are presented and compared. In a companion paper (Part II of this work), the phase and damping properties of the developed schemes are analysed and numerical examples are included to confirm the effectiveness of the proposed methodology for solving time-dependent convection-diffusion-reaction problems. |
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Abstract:
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Peer Reviewed |
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Materia(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
-Finite element method
-Spatial analysis
-convection-diffusion-reaction
-time-stepping schemes
-stabilization
-least squares
-finite element method
-Elements finits, Mètode dels -- Anàlisi numèrica |
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Derechos:
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Tipo de documento:
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Artículo - Versión presentada
Artículo |
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