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

Zhendong Luo, Fei Teng and Jing Chen

Mathematics and Computers in Simulation (MATCOM), 2018, vol. 146, issue C, 118-133

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.

Keywords: Proper orthogonal decomposition; Reduced-order Crank–Nicolson finite volume element extrapolating algorithm; Two-dimensional Sobolev equations; Error estimate (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:146:y:2018:i:c:p:118-133

DOI: 10.1016/j.matcom.2017.11.002

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