Error estimates of an operator‐splitting finite element method for the time‐dependent natural convection problem

Yun‐Bo Yang; Bin‐Chao Huang; Yao‐Lin Jiang

doi:10.1002/num.22963

journal article Nov 24, 2022

Error estimates of an operator‐splitting finite element method for the time‐dependent natural convection problem

Yun‐Bo Yang

Bin‐Chao Huang Yao‐Lin Jiang

Numerical Methods for Partial Differential Equations Vol. 39 No. 3 pp. 2202-2226 · Wiley

View at Publisher Save 10.1002/num.22963

Abstract

AbstractIn this article, an operator‐splitting (or a fractional‐step) finite element method is proposed for the numerical solution of the time‐dependent natural convection problem. We first analyze the time‐discrete fractional‐step scheme, which decouples the considered system into three subproblems, and each subproblem can be solved more easily than the original one. Under some mild regularity assumptions, the stability and error estimates for the velocity and the temperature are established rigorously. In addition, a full discrete fractional‐step scheme based on the time‐discrete scheme is proposed and the rigorous error analysis is presented. We derive the temporal–spatial error estimates of for the velocity and the temperature in the discrete space under the constraint Δt ≥ Ch. Numerical experiments are performed to confirm the theoretical predictions and demonstrate the efficiency of the method.

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Metrics

9

Citations

45

References

Details

Published: Nov 24, 2022
Vol/Issue: 39(3)
Pages: 2202-2226
License: View

Authors

Y

Yun‐Bo Yang

Department of Mathematics Yunnan Normal University Kunming People's Republic of China; Key Laboratory of Complex System Modeling and Application for Universities in Yunnan Kunming People's Republic of China

B

Bin‐Chao Huang

Department of Mathematics Yunnan Normal University Kunming People's Republic of China

Y

Yao‐Lin Jiang

Department of Mathematics Yunnan Normal University Kunming People's Republic of China; School of Mathematics and Statistics Xi'an Jiaotong University Xi'an People's Republic of China

Funding

Innovative Research Group Project of the National Natural Science Foundation of China Award: 12161095

Cite This Article

Yun‐Bo Yang, Bin‐Chao Huang, Yao‐Lin Jiang (2022). Error estimates of an operator‐splitting finite element method for the time‐dependent natural convection problem. Numerical Methods for Partial Differential Equations, 39(3), 2202-2226. https://doi.org/10.1002/num.22963

Error estimates of an operator‐splitting finite element method for the time‐dependent natural convection problem

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