Analysis of a Galerkin-characteristic finite element method for convection-diffusion problems in porous media

Abstract

We present a Galerkin-characteristic finite element method for the numerical solution of time-dependent convection-diffusion problems in porous media. The proposed method allows the use of equal-order finite element approximations for all solutions in the problem. In addition, the standard Courant-Friedrichs-Lewy condition is relaxed with the Lagrangian treatment of convection terms, and the time truncation errors are reduced in the diffusion-reaction part. Analysis of convergence and stability of the proposed method is also investigated in this study and error estimates in the $$${L}$$$2-norm are established for the numerical solutions. Numerical performance of the method is examined using two examples to verify the theoretical estimates and to demonstrate the high accuracy and efficiency of the proposed Galerkin-characteristic finite element method.