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Wang, Tongli; Zhao, Jikun

Error analysis of nonconforming virtual element method for Stokes problem with low regularity. (English) Zbl 1528.65118

Taiwanese J. Math. 27, No. 4, 719-735 (2023).
Summary: In this paper, the nonconforming virtual element method is used to solve the Stokes problem where the velocity and pressure are allowed to have the low regularity. With the help of an enriching operator, the consistency error is estimated under the low regularity condition. Then the optimal error estimates are obtained for the velocity and pressure approximations, which implies that the nonconforming virtual element method has the good convergence even for the Stokes problem with the low regularity.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows
76M10 Finite element methods applied to problems in fluid mechanics
35Q35 PDEs in connection with fluid mechanics

Keywords:

nonconforming virtual element; polygonal mesh; Stokes equation
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References:

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