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A POD-based reduced-order Crank–Nicolson finite volume element extrapolating algorithm for 2D Sobolev equations

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  • Luo, Zhendong
  • Teng, Fei
  • Chen, Jing

Abstract

Based on proper orthogonal decomposition (POD), a new type of reduced-order Crank–Nicolson finite volume element extrapolating algorithm (CNFVEEA) including very few degrees of freedom but holding fully second-order accuracy for two-dimensional (2D) Sobolev equations is established firstly. Then, the error estimates of POD-based reduced-order CNFVEEA solutions are provided, which acted as a suggestion for choosing number of POD basis and a criterion for updating POD basis, and the procedure for the implementation of the POD-based reduced-order CNFVEEA is given. Finally, a numerical example is presented illustrating that the numerical computational conclusions are consistent with theoretical ones. Moreover, it is shown that the POD-based reduced-order CNFVEEA is very suitable to finding numerical solutions of 2D Sobolev equations and is better than the POD-based FVE formulation with first-order accuracy in time.

Suggested Citation

  • Luo, Zhendong & Teng, Fei & Chen, Jing, 2018. "A POD-based reduced-order Crank–Nicolson finite volume element extrapolating algorithm for 2D Sobolev equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 118-133.
    • Handle: RePEc:eee:matcom:v:146:y:2018:i:c:p:118-133
    DOI: 10.1016/j.matcom.2017.11.002
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    References listed on IDEAS

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    1. Luo, Zhendong & Li, Hong & Sun, Ping & An, Jing & Navon, Ionel Michael, 2013. "A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 50-68.
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    Cited by:

    1. Zhendong Luo, 2020. "The Reduced-Order Extrapolating Method about the Crank-Nicolson Finite Element Solution Coefficient Vectors for Parabolic Type Equation," Mathematics, MDPI, vol. 8(8), pages 1-11, August.

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