Accurate FIC-FEM formulation for the multidimensional steady-state advection diffusion–absorption equation

Published in Comput. Methods Appl. Mech. Engrg, Vol. 327, pp. 352-368, 2017
doi: 10.1016/j.cma.2017.08.012

Abstract

In this paper we present an accurate stabilized FIC-FEM formulation for the multidimensional steady-state advection-diffusion-absorption equation. The stabilized formulation is based on the Galerkin FEM solution of the governing differential equations derived via the Finite Increment Calculus (FIC) method using two stabilization parameters. The value of the two stabilization parameters ensuring an accurate nodal FEM solution using uniform meshes of linear elements is obtained from the optimal values for the 1D problem. The accuracy of the new FIC-FEM formulation is demonstrated in the solution of 2D steadystate advection-diffusion-absorption problems for a range of physical parameters and boundary conditions.

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