A reduced-order extrapolated Crank–Nicolson finite spectral element method based on POD for the 2D non-stationary Boussinesq equations

Abstract In this paper, we mainly utilize proper orthogonal decomposition (POD) to reduce the order for the coefficient vector of the classical Crank–Nicolson finite spectral element (CCNFSE) method of the two-dimensional (2D) non-stationary Boussinesq equations about vorticity-stream functions so that the reduced-order method maintains all the advantages of the CCNFSE method. Toward this end, we first establish a CCNFSE format with the second-order time accuracy for the two-dimensional (2D) non-stationary Boussinesq equations about vorticity-stream functions and analyze the existence, stability, and convergence of the CCNFSE solutions. And then, by POD, we establish a reduced-order extrapolated Crank–Nicolson finite spectral element (ROECNFSE) method and analyze the existence, stability, and convergence of the ROECNFSE solutions as well as offer the flowchart for seeking ROECNFSE solutions. Finally, we use two sets of numerical experiments to validate that the numerical computational consequences are accorded with the theoretical ones such that the effectiveness and feasibility of the ROECNFSE method are further verified. Both theory and method in this paper is new and completely different from the existing reduced-order methods.

• Publication year

  2019

• Venue

  Journal of Mathematical Analysis and Applications

• Publication date

  2019-03-01

• Fields of study

  Mathematics, Physics, Engineering

• Identifiers
  DOI 10.1016/J.JMAA.2018.10.092
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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