LUO Zhen-dong, OU Qiu-lan, XIE Zheng-hui. A Reduced Finite Difference Scheme and Error Estimates Based on POD Method for the Non-Stationary Stokes Equation[J]. Applied Mathematics and Mechanics, 2011, 32(7): 795-806. doi: 10.3879/j.issn.1000-0887.2011.07.004
Citation: LUO Zhen-dong, OU Qiu-lan, XIE Zheng-hui. A Reduced Finite Difference Scheme and Error Estimates Based on POD Method for the Non-Stationary Stokes Equation[J]. Applied Mathematics and Mechanics, 2011, 32(7): 795-806. doi: 10.3879/j.issn.1000-0887.2011.07.004

A Reduced Finite Difference Scheme and Error Estimates Based on POD Method for the Non-Stationary Stokes Equation

doi: 10.3879/j.issn.1000-0887.2011.07.004
  • Received Date: 2011-03-24
  • Rev Recd Date: 2011-04-25
  • Publish Date: 2011-07-15
  • The properorthogonal decom position (POD) was amodel reduction technique for the simulation of physical processes governed by partial differen tial equations, e. g. fluid flows. It was success fully used in the reduced-ordermodeling of complex systems. The applications of POD method were extended, i. e., apply POD method to a classical finited ifference (FD) scheme for the non-stationary Stokes equation with real practical applied background, estab lish a reduced FD scheme with lowerd imensions and sufficiently high accuracy, and provide the errorestmi ates between the reduced FD solutions and the classical FD solutions. Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced FD schemebased on POD method is feasible and efficient for solving FD scheme for the non-stationary Stokes equation.
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