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Títol:	An accurate FIC-FEM formulation for the 1D convection-diffusion-reaction equation
Autor/a:	Oñate Ibáñez de Navarra, Eugenio; Miquel Canet, Juan; Nadukandi, Prashanth
Altres autors:	Universitat Politècnica de Catalunya. Departament de Resistència de Materials i Estructures a l'Enginyeria; Universitat Politècnica de Catalunya. GMNE - Grup de Mètodes Numèrics en Enginyeria; Universitat Politècnica de Catalunya. RMEE - Grup de Resistència de Materials i Estructures en l'Enginyeria
Abstract:	In this paper we present an accurate stabilized FIC-FEM formulation for the 1D advection-diffusion-reaction equation in the exponential and propagation regimes using two stabilization parameters. Both the steady-state and transient solutions are considered. The stabilized formulation is based on the standard Galerkin FEM solution of the governing differential equations derived via the Finite Increment Calculus (FIC) method. The steady-state problem is considered first. The optimal value of the two stabilization parameters ensuring an exact (nodal) FEM solution using uniform meshes of linear 2-noded elements is obtained. In the absence of the absorption term the formulation simplifies to the standard one-parameter Petrov-Galerkin method for the advection-diffusion problem. For the diffusion-reaction case one stabilization parameter is just needed and the diffusion-type stabilization term is identical to that obtained by Felippa and Oñate (2007) using a variational FIC approach. A procedure for computing the stabilization parameters for the transient problem is proposed. The accuracy of the new FIC-FEM formulation is demonstrated in the solution of steady-state and transient 1D advection-diffusion-radiation problems for a the range of physical parameters and boundary conditions. Finally we outline the procedure to extend the 1D FIC-FEM formulation to multidimensions.
Abstract:	Peer Reviewed
Matèries:	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits -One-dimensional flow -Finite element method--Mathematical models -Finite element method -Stabilized formulation -Convection-diffusion-reaction -Finite increment calculus -Finite calculus -FIC -One dimensional problem -COMP-DES-MAT Project -COMPDESMAT Project -Elements finits, Mètode dels
Drets:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Tipus de document:	Article - Versió presentada Article
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