A Quadratic Serendipity Finite Volume Element Method on Arbitrary Convex Polygonal Meshes  

作　　者：Yanlong Zhang 

机构地区：[1]Graduate School of China Academy of Engineering Physics,Beijing,100088,P.R.China [2]Institute of Applied Physics and Computational Mathematics,Beijing,100088,P.R.China

出　　处：《Communications in Computational Physics》2023年第6期116-131,共16页计算物理通讯（英文）

基　　金：supported by the National Natural Science Foundation of China(Nos.11871009,12271055);the Foundation of LCP and the Foundation of CAEP(CX20210044).

摘　　要：Based on the idea of serendipity element,we construct and analyze the first quadratic serendipity finite volume element method for arbitrary convex polygonalmeshes in this article.The explicit construction of quadratic serendipity element shape function is introduced from the linear generalized barycentric coordinates,and the quadratic serendipity element function space based on Wachspress coordinate is selected as the trial function space.Moreover,we construct a family of unified dual partitions for arbitrary convex polygonal meshes,which is crucial to finite volume element scheme,and propose a quadratic serendipity polygonal finite volume element method with fewer degrees of freedom.Finally,under certain geometric assumption conditions,the optimal H1 error estimate for the quadratic serendipity polygonal finite volume element scheme is obtained,and verified by numerical experiments.

关 键 词：Quadratic serendipity polygonal finite volume element method arbitrary convex polygonal meshes Wachspress coordinate unified dual partitions optimal H1 error estimate 

分 类 号：O17[理学—数学]