TY - JOUR
T1 - A Quadratic Serendipity Finite Volume Element Method on Arbitrary Convex Polygonal Meshes
AU - Zhang , Yanlong
JO - Communications in Computational Physics
VL - 1
SP - 116
EP - 131
PY - 2023
DA - 2023/08
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2022-0307
UR - https://global-sci.org/intro/article_detail/cicp/21882.html
KW - Quadratic serendipity polygonal finite volume element method, arbitrary convex polygonal meshes, Wachspress coordinate, unified dual partitions, optimal $H^1$ error estimate.
AB - <p style="text-align: justify;">Based on the idea of serendipity element, we construct and analyze the
first quadratic serendipity finite volume element method for arbitrary convex polygonal meshes 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 $H^1$ error estimate for the quadratic serendipity
polygonal finite volume element scheme is obtained, and verified by numerical experiments.</p>