TY - JOUR
T1 - A Cell-Centered Finite Element Method with Imposed Flux Continuity and Streamline Upwind Technique for Advection-Diffusion Problems on General Meshes
AU - Hai , Ong Thanh
AU - Thai , Nguyen T. Hong
AU - Thanh , Tran Thien
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 401
EP - 431
PY - 2025
DA - 2025/03
SN - 22
DO - http://doi.org/10.4208/ijnam2025-1018
UR - https://global-sci.org/intro/article_detail/ijnam/23885.html
KW - Advection-diffusion equations, anisotropic and heterogeneous diffusion, convection-dominated regime, cell-centered schemes, and convergence analysis.
AB - <p style="text-align: justify;">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.</p>