A formal construction of a divergence-free basis in the nonconforming virtual element method for the Stokes problem

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We develop a formal construction of a pointwise divergence-free basis in the nonconforming virtual element method of arbitrary order for the Stokes problem introduced in Zhao et al. (SIAM J. Numer. Anal. 57(6):2730-2759, 2019). The proposed construction can be seen as a generalization of the divergence-free basis in Crouzeix-Raviart finite element space (Brenner, Math. Comp. 55(192):411-437, 1990; Thomasset, 1981) to the virtual element space. Using the divergence-free basis obtained from our construction, we can eliminate the pressure variable from the mixed system and obtain a symmetric positive definite system. Several numerical tests are presented to confirm the efficiency and the accuracy of our construction.
Publisher
SPRINGER
Issue Date
2022-09
Language
English
Article Type
Article
Citation

NUMERICAL ALGORITHMS, v.91, no.1, pp.449 - 471

ISSN
1017-1398
DOI
10.1007/s11075-022-01269-z
URI
http://hdl.handle.net/10203/297963
Appears in Collection
MA-Journal Papers(저널논문)
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