Acta mathematica scientia, Series B >
A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS
Received date: 2013-04-30
Revised date: 2013-10-12
Online published: 2014-05-20
Supported by
Research of this work was mainly supported by the National Science Foundation of China (11271127, 11361035), Science Research of Guizhou Education Department (QJHKYZ[2013]207), and Natural Science Foundation of Inner Mongolia (2012MS0106).
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.
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 . DOI: 10.1016/S0252-9602(14)60056-4
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