A reduced-order Crank–Nicolson finite volume element formulation based on POD method for parabolic equations

In this paper, a proper orthogonal decomposition (POD) method is used to deal with a classical Crank–Nicolson finite volume element (CNFVE) method for two-dimensional parabolic equations. A reduced-order CNFVE formulation with lower dimensions and sufficiently high accuracy based on POD technique is established, the error estimates between reduced-order CNFVE solutions based on the POD method and classical CNFVE solutions are provided, and the extrapolation algorithm for solving reduced-order CNFVE formulation is implemented. Some numerical examples show that the results of numerical computation are consistent with previous theoretical conclusions. Moreover, it is shown that the reduced-order CNFVE formulation based on POD method is feasible and efficient for solving two-dimensional parabolic equations.