A NEW REDUCED-ORDER FVE ALGORITHM BASED ON POD METHOD FOR VISCOELASTIC EQUATIONS

doi:10.1016/S0252-9602(13)60065-X

Abstract

Abstract:

A proper orthogonal decomposition (POD) technique is used to reduce the finite volume element (FVE) method for two-dimensional (2D) viscoelastic equations. A reduced-order fully discrete FVE algorithm with fewer degrees of freedom and sufficiently high accuracy based on POD method is established. The error estimates of the reduced-order fully discrete FVE solutions and the implementation for solving the reduced-order fully discrete FVE algorithm are provided. Some numerical examples are used to illus-trate that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order fully discrete FVE algorithm is one of the most effective numerical methods by comparing with corresponding numerical results of finite element formulation and finite difference scheme and that the reduced-order fully discrete FVE algorithm based on POD method is feasible and efficient for solving 2D viscoelastic equations.

Key words: proper orthogonal decomposition, finite volume element method, viscoelastic equations, error estimate

CLC Number:

65N30

LI Hong, LUO Zhen-Dong, GAO Jun-Qiang. A NEW REDUCED-ORDER FVE ALGORITHM BASED ON POD METHOD FOR VISCOELASTIC EQUATIONS[J].Acta mathematica scientia,Series B, 2013, 33(4): 1076-1098.

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