A Cell-Centered Finite Element Method with Imposed Flux Continuity and Streamline Upwind Technique for Advection-Diffusion Problems on General Meshes
Year: 2025
Author: Ong Thanh Hai, Nguyen T. Hong Thai, Tran Thien Thanh
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 3 : pp. 401–431
Abstract
We extend the cell-centered finite element method (CCFE) [1] with imposed flux continuity and streamline upwind technique to solve the advection-diffusion equations with anisotropic and heterogeneous diffusivity and a convection-dominated regime on general meshes. The scheme is cell-centered in the sense that the solution is computed by cell unknowns of the primal mesh. From general meshes, the method is constructed by the dual meshes and their triangular submeshes. The scheme gives auxiliary edge unknowns interpolated by the multipoint fluid approximation technique to obtain the local continuity of numerical fluxes across the interfaces. In addition, the scheme uses piecewise linear functions combined with a streamline upwind technique on the dual submesh in order to stabilize the numerical solutions and eliminate the spurious oscillations. The coercivity, the strong and dual consistency, and the convergence properties of this method are shown in the rigorous theoretical framework. Numerical results are carried out to highlight accuracy and computational cost.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2025-1018
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 3 : pp. 401–431
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Advection-diffusion equations anisotropic and heterogeneous diffusion convection-dominated regime cell-centered schemes and convergence analysis.
Author Details
Ong Thanh Hai Email
Nguyen T. Hong Thai Email
Tran Thien Thanh Email