Year: 2023
Author: Yanlong Zhang
Communications in Computational Physics, Vol. 34 (2023), Iss. 1 : pp. 116–131
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0307
Communications in Computational Physics, Vol. 34 (2023), Iss. 1 : pp. 116–131
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Quadratic serendipity polygonal finite volume element method arbitrary convex polygonal meshes Wachspress coordinate unified dual partitions optimal $H^1$ error estimate.