FIC–FEM formulation for the multidimensional transient advection–diffusion–absorption equation

Abstract

In this paper we present a stabilized FIC–FEM formulation for the multidimensional transient advection–diffusion–absorption equation. The starting point is the non-local form of the governing equations for the multidimensional transient advection–diffusion–absorption problems obtained via the Finite Increment Calculus (FIC) procedure. The FIC governing equations have a residual form that introduces a characteristic length vector that depends on streamline, absorption and shock capturing stabilization parameters, as well as on a characteristic element size that ensures a stabilized numerical solution using a standard Galerkin FEM. The value of the stabilization parameters is obtained as an extension of the steady-state form. The accuracy of the FIC–FEM formulation is verified in the solution of several transient advection–diffusion–absorption problems using regular meshes of 3-noded triangles and 4-noded quadrilaterals.