TY - JOUR
T1 - An Adaptive Polygonal Finite Volume Element Method Based on the Mean Value Coordinates for Anisotropic Diffusion Problems
AU - Zhang , Yanlong
AU - Wu , Jiming
JO - Communications in Computational Physics
VL - 3
SP - 783
EP - 809
PY - 2025
DA - 2025/03
SN - 37
DO - http://doi.org/10.4208/cicp.OA-2023-0213
UR - https://global-sci.org/intro/article_detail/cicp/23922.html
KW - Polygonal finite volume element method, mean value coordinates, hanging nodes, adaptive algorithm.
AB - <p style="text-align: justify;">We propose a polygonal finite volume element method based on the mean
value coordinates for anisotropic diffusion problems on star-shaped polygonal meshes.
Because the convex cells with hanging nodes are always star-shaped, the computation
on them is no longer a problem. Naturally, we apply this advantage of the new polygonal finite volume element method to construct an adaptive polygonal finite volume element algorithm. Moreover, we introduce two refinement strategies, called quadtree-based refinement strategy and polytree-based refinement strategy respectively, and
they all have great performance in our numerical tests. The new adaptive algorithm
allows the use of hanging nodes, and the number of hanging nodes on each edge is
unrestricted in general. Finally, several numerical examples are provided to show the
convergence and efficiency of the proposed method on various polygonal meshes. The
numerical results also show that the new adaptive algorithm not only reduces the computational cost and the implementation complexity in mesh refinement, but also ensures the accuracy and convergence.</p>