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| This paper considers a second-order projection scheme for solving the Kelvin-Voigt problem using the Crank-Nicolson scheme. The backward Euler scheme is employed for the time derivative term, while a semi-implicit scheme is used for the nonlinear term discretization. To enhance computational efficiency, a projection method is adopted to decouple velocity and pressure, thereby decomposing the considered model into two linear sub-problems, thereby simplifying the problem solution. The paper provides stability and convergence analysis of the numerical solution, demonstrating that the numerical scheme is unconditionally stable under certain conditions on the stabilization factor, and the errors of the velocity field in the L2 and H1 norms are second-order and first-order, respectively. Finally, the effectiveness of the numerical scheme is verified through numerical examples. |
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| Keywords:Computational mathematics. Kelvin-Voigt. Second-order projection. Crank-Nicolson. |
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