Research Communication | Open Access
Volume 2021 | Communication ID 211
Volume 2021 | Communication ID 211
| A Semi-Lagrangian Finite Element Method for Darcy-Convection-Diffusion Problems: Analysis and Numerical Simulation |
Loubna Salhi, Mofdi El-Amrani, Mohammed Seaid
Received |
Accepted |
Published |
January 31, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: We present a semi-Lagrangian finite element method for the numerical solution of time-dependent coupled Darcy-convection-diffusion problems. The proposed method allows the use of equal-order finite element approximations for all solutions in the problem. In addition, due to the Lagrangian treatment of convection terms in the considered problems, the standard Courant-Friedrichs-Lewy condition is relaxed, and the time truncation errors are reduced in the diffusion-reaction part. Analysis of stability and convergence is also investigated in this study and error estimates in the L2-norm are ...