Affiliations: [a] Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR, USA | [b] Department of Mathematics, University of Al-Qadisiyah, Al Diwaniyah, Iraq | [c] Department of Mathematics and Physics, Texas A&M International University, Laredo, TX, USA | [d] Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR, USA | [e] Ministry of Education, General Directorate of Education in Basrah, Iraq
Correspondence:
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Corresponding author: Ahmed Al-Taweel, Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA. E-mail: [email protected].
Note: [1] This research was supported by a Texas A&M International University Research Grant.
Abstract: In this paper, we propose a stabilizer free spatial weak Galerkin (SFSWG) finite element method for solving time-dependent convection diffusion equations based on weak form Eq. (4). SFSWG method in spatial direction and Euler difference operator Eq. (37) in temporal direction are used. The main reason for using the SFSWG method is because of its simple formulation that makes this algorithm more efficient and its implementation easier. The optimal rates of convergence of 𝒪(hk) and 𝒪(hk+1) in a discrete H1 and L2 norms, respectively, are obtained under certain conditions if polynomial spaces (Pk(K),Pk(e),[Pj(K)]2) are used in the SFSWG finite element method. Numerical experiments are performed to verify the effectiveness and accuracy of the SFSWG method.