Year: 2024
Author: Xin Liu, Qixuan Song, Yu Gao, Zhangxin Chen
Communications in Computational Physics, Vol. 36 (2024), Iss. 1 : pp. 221–247
Abstract
In this paper, we develop and analyze two stabilized mixed virtual element schemes for the Stokes problem based on the lowest-order velocity-pressure pairs (i.e., a piecewise constant approximation for pressure and an approximation with an accuracy order $k = 1$ for velocity). By applying local pressure jump and projection stabilization, we ensure the well-posedness of our discrete schemes and obtain the corresponding optimal $H^1$- and $L^2$-error estimates. The proposed schemes offer a number of attractive computational properties, such as, the use of polygonal/polyhedral meshes (including non-convex and degenerate elements), yielding a symmetric linear system that involves neither the calculations of higher-order derivatives nor additional coupling terms, and being parameter-free in the local pressure projection stabilization. Finally, we present the matrix implementations of the essential ingredients of our stabilized virtual element methods and investigate two- and three-dimensional numerical experiments for incompressible flow to show the performance of these numerical schemes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0233
Communications in Computational Physics, Vol. 36 (2024), Iss. 1 : pp. 221–247
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Stokes equations stabilized virtual element scheme pressure jump pressure projection polygonal meshes.