A defect correction weak Galerkin finite element method for the Kelvin-Voigt viscoelastic fluid flow model. (English) Zbl 07890930
Summary: In this paper, we present a defect correction weak Galerkin finite element method for solving the Kelvin-Voigt viscoelastic fluid flow model, which can guarantee that the discrete velocity is globally divergence-free. The second-order Crank-Nicolson difference scheme is considered for temporal discretization. In particular, combined with the defect correction method, the numerical oscillation effect is reduced at high Reynolds number. Our algorithm not only gives the stability and convergence of the numerical solutions of velocity and pressure but also is uniformly valid at the retardation time \(\kappa \to 0\). Several numerical experiments are performed to verify the method has good behaviors.
MSC:
| 65Nxx | Numerical methods for partial differential equations, boundary value problems |
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 76Mxx | Basic methods in fluid mechanics |
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