TY  - Type of reference 
TI  - Analysis of a Galerkin-characteristic finite element method for convection-diffusion problems in porous media 
AU  - Loubna Salhi 
AU  - Mofdi El-Amrani 
AU  - Mohammed Seaid 
AB  - 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. 
DO  - 10.21494/ISTE.OP.2021.0700 
JF  - Advances in Pure and Applied Mathematics 
KW  - Convection-diffusion problems,  Darcy equation,  Porous media,  Galerkin-characteristic method,  Finite elements,  A priori error estimates, Problémes de convection-diffusion,  Équation de Darcy,  Milieux poreux,  Méthode semi-lagrangienne,  éléments finis,  Estimation des erreurs a priori,  
L1  - https://openscience.fr/IMG/pdf/iste_apam21v12nspe_6.pdf 
LA  - en 
PB  - ISTE OpenScience 
DA  - 2021/07/28 
SN  - 1869-6090 
TT  - L’analyse d’une méthode semi-lagrangienne et éléments finis pour les problémes de convection-diffusion en milieux poreux 
UR  - https://openscience.fr/Analysis-of-a-Galerkin-characteristic-finite-element-method-for-convection 
IS  - Issue 3 (Special AUS-ICMS 2020) 
VL  - 12 
ER  -