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

2021/08/23 by Kwak, Do Y., Park, Hyeokjoo
#65N12 #65N30 #76D07 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2108.09967

Abstract

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 [19]. The proposed construction can be seen as a generalization of the divergence-free basis in Crouzeix-Raviart finite element space [10, 17] 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.

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