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

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.This research was partially funded by the PRECISE, Spain project (BIA2017-83805-R) of the National Research Plan of the Spanish Government. Support for this work was also provided from the Office for Naval Research Global (ONRG) of the US Navy through the NICE-SHIP project.The authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness through the Severo Ochoa Programme for Centres of Excellence in RTD (CEX2018-000797-S). We also acknowledge the financial support of the CERCA programme of the Generalitat de Catalunya (Spain).Peer Reviewe