New Superconvergent Structures with Optional Superconvergent Points for the Finite Volume Element Method
Year: 2023
Author: Xiang Wang, Yuqing Zhang, Zhimin Zhang
Communications in Computational Physics, Vol. 33 (2023), Iss. 5 : pp. 1332–1356
Abstract
New superconvergent structures are proposed and analyzed for the finite volume element (FVE) method over tensorial meshes in general dimension $d$ (for $d≥2$); we call these orthogonal superconvergent structures. In this framework, one has the freedom to choose the superconvergent points of tensorial $k$-order FVE schemes (for $k≥3$). This flexibility contrasts with the superconvergent points (such as Gauss points and Lobatto points) for current FE schemes and FVE schemes, which are fixed. The orthogonality condition and the modified M-decomposition (MMD) technique that are developed over tensorial meshes help in the construction of proper superclose functions for the FVE solutions and in ensuring the new superconvergence properties of the FVE schemes. Numerical experiments are provided to validate our theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0295
Communications in Computational Physics, Vol. 33 (2023), Iss. 5 : pp. 1332–1356
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Superconvergence finite volume orthogonality condition tensorial mesh rectangular mesh.