Abstract
In this article, we employ proper orthogonal decomposition (POD) technique to establish a POD-based reduced-order stabilized mixed finite volume element (SMFVE) extrapolation algorithm based on two local Gaussian integrals, parameter-free, and Crank-Nicolson (CN) method with fewer degrees of freedom for the non-stationary Navier-Stokes equations. The error estimates between the POD-based reduced-order SMFVE solutions and the classical SMFVE solutions and the implementation for the POD-based reduced-order SMFVE extrapolation algorithm are provided. A numerical example is used to illustrate that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the POD-based reduced-order SMFVE extrapolation algorithm is feasible and efficient for finding numerical solutions for the non-stationary Navier-Stokes equations.
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