A quadratic finite volume element method for anisotropic diffusion problems on polygonal meshes
发布时间：2026-05-13
点击次数：
DOI码：10.1016/j.jcp.2026.115009
发表刊物：Journal of Computational Physics
摘要：It is well-known that finite volume element method (FVEM) often requires restrictive geometric mesh constraints to achieve high-order accuracy. This paper presents a novel quadratic FVEM scheme designed specifically for solving anisotropic diffusion problems on general polygonal meshes. The relaxation of mesh shape requirements is achieved through innovations in both trial and test function spaces. The main contribution of this paper can be summarized as follows. Firstly, an enriched cubic polynomial trial space is constructed in each cell by augmenting standard quadratic finite element degrees of freedom (vertex and edge-midpoint values) with carefully chosen internal moments. This enrichment significantly boosts accuracy while demanding only minimal mesh regularity assumptions. Crucially, these auxiliary internal variables are efficiently localized through a cell-level condensation technique, preserving the sparsity structure and primary degrees of freedom count of a standard quadratic finite element method. Secondly, a flexible dual partition strategy employing edge duplication is developed, which enables us to handle general polygonal shapes without geometric restrictions. To the best of our knowledge, this constitutes the first quadratic FVEM scheme applicable to general polygonal meshes. With the help of classical Picard iteration, our method is successfully extended to solve semilinear elliptic equation defined in an irregular domain featuring an NACA 0012 airfoil. Finally, numerical experiments confirm the optimal convergence rates of the proposed scheme: second-order in the H1-norm and third-order in the L2-norm. Furthermore, the proposed scheme demonstrates significantly improved robustness to severe mesh distortion compared to existing methods.
合写作者：Xiaoxin Wu, Yufeng Xu, Kejia Pan
论文类型：期刊论文
学科门类：理学
一级学科：数学
文献类型：J
卷号：562
页面范围：1--20
是否译文：否
发表时间：2026-05-05
收录刊物：SCI
发布期刊链接：https://www.sciencedirect.com/science/article/pii/S0021999126003621