A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS

doi:10.1016/S0252-9602(14)60056-4

Abstract

Abstract:

In this article, a proper orthogonal decomposition (POD) method is used to study a classical splitting positive definite mixed finite element (SPDMFE) formulation for second-order hyperbolic equations. A POD reduced-order SPDMFE extrapolating algorithm with lower dimensions and sufficiently high accuracy is established for second-order hyperbolic equations. The error estimates between the classical SPDMFE solutions and the reduced-order SPDMFE solutions obtained from the POD reduced-order SPDMFE extrapolating algorithm are provided. The implementation for solving the POD reduced-order SPDMFE extrapolating algorithm is given. Some numerical experiments are presented illustrating that the results of numerical computation are consistent with theoretical conclusions, thus validating that the POD reduced-order SPDMFE extrapolating algorithm is feasible and efficient for solving second-order hyperbolic equations.

Key words: Proper orthogonal decomposition, splitting positive definite mixed finite ele-ment formulation, hyperbolic equations, error estimate

CLC Number:

65N30

LUO Zhen-Dong, LI Hong. A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS[J].Acta mathematica scientia,Series B, 2014, 34(3): 872-890.

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