Published in Computer Methods in Applied Mechanics and Engineering, Vol. 298, pp. 373-406, 2016
doi: 10.1016/j.cma.2015.09.022

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 [16] 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.

Full document

The PDF file did not load properly or your web browser does not support viewing PDF files. Download directly to your device: Download PDF document
Back to Top

Document information

Published on 01/01/16
Submitted on 20/11/17

DOI: 10.1016/j.cma.2015.09.022
Licence: CC BY-NC-SA license

Document Score

0

Times cited: 2
Views 41
Recommendations 0

Share this document

claim authorship

Are you one of the authors of this document?