Back to Search
Start Over
A reduced-order extrapolated Crank–Nicolson finite spectral element method based on POD for the 2D non-stationary Boussinesq equations
- Source :
- Journal of Mathematical Analysis and Applications. 471:564-583
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
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.
- Subjects :
- Flowchart
Applied Mathematics
010102 general mathematics
Spectral element method
01 natural sciences
Stability (probability)
law.invention
010101 applied mathematics
Point of delivery
law
Convergence (routing)
Order (group theory)
Crank–Nicolson method
Applied mathematics
0101 mathematics
Element (category theory)
Analysis
Mathematics
Subjects
Details
- ISSN :
- 0022247X
- Volume :
- 471
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Analysis and Applications
- Accession number :
- edsair.doi...........94e8c94b3667bec0da6f1b25444aed0d