Malaysian Journal of Mathematical Sciences, September 2024, Vol. 18, No. 3
Streamline Diffusion Weak Galerkin Finite Element Methods for Linear Unsteady State Convection Diffusion Equations and Error Analysis
Abed, I. A. and Kashkool, H. A.
Corresponding Email: [email protected]
Received date: 19 January 2024
Accepted date: 10 June 2024
Abstract:
In this paper, the streamline diffusion weak Galerkin finite element method is proposed and analyzed for solving unsteady time convection diffusion problem in two dimension. The v-elliptic property and the stability of this scheme are proved in terms of some conditions. We derive an error estimate in $L^2(\mu)$ and $H^1(\mu)$ norm. Numerical experiments have demonstrated the effectiveness of the method in solving convection propagation problems, and the theoretical analysis has been validated.
Keywords: streamline diffusion; weak Galerkin finite element; discrete gradient; stability; error analysis
