A weak Galerkin finite element method for solving nonlinear convection-diffusion problems in two dimensions

Mohammed S. Cheichan, Hashim A. Kashkool and Fuzheng Gao

Applied Mathematics and Computation, 2019, vol. 354, issue C, 149-163

Abstract: We study weak Galerkin (WG) finite element method (FEM) for solving nonlinear convection-diffusion problems. A WG finite element scheme is presented based on a new variational form. We prove the energy conservation law and stability of the continuous time WG FEM. In particular, optimal order error estimates are established for the WG FEM approximation in both a discrete H1-norm and L2-norm. Numerical experiments are performed to confirm the theoretical results.

Keywords: Weak Galerkin; Finite element method; Nonlinear convection-diffusion problem; Energy conservation; Stability; Error estimate (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:354:y:2019:i:c:p:149-163

DOI: 10.1016/j.amc.2019.02.043

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