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Volume 19, Issue 6
A Decoupled, Parallel, Iterative Finite Element Method for Solving the Steady Boussinesq Equations

Yuanyuan Hou, Wenjing Yan, Lioba Boveleth & Xiaoming He

Int. J. Numer. Anal. Mod., 19 (2022), pp. 739-760.

Published online: 2022-09

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  • Abstract

In this work, a decoupled, parallel, iterative finite element method for solving the steady Boussinesq equations is proposed and analyzed. Starting from an initial guess, an iterative algorithm is designed to decouple the Naiver-Stokes equations and the heat equation based on certain explicit treatment with the solution from the previous iteration step. At each step of the iteration, the two equations can be solved in parallel by using finite element discretization. The existence and uniqueness of the solution to each step of the algorithm is proved. The stability analysis and error estimation are also carried out. Numerical tests are presented to verify the analysis results and illustrate the applicability of the proposed method.

  • Keywords

Steady Boussinesq equations, decoupled parallel iterative algorithm, finite element method, error analysis.

  • AMS Subject Headings

35Q30, 65N12, 65N15, 65N30, 76D05, 76R10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-739, author = {Hou , YuanyuanYan , WenjingBoveleth , Lioba and He , Xiaoming}, title = {A Decoupled, Parallel, Iterative Finite Element Method for Solving the Steady Boussinesq Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {6}, pages = {739--760}, abstract = {

In this work, a decoupled, parallel, iterative finite element method for solving the steady Boussinesq equations is proposed and analyzed. Starting from an initial guess, an iterative algorithm is designed to decouple the Naiver-Stokes equations and the heat equation based on certain explicit treatment with the solution from the previous iteration step. At each step of the iteration, the two equations can be solved in parallel by using finite element discretization. The existence and uniqueness of the solution to each step of the algorithm is proved. The stability analysis and error estimation are also carried out. Numerical tests are presented to verify the analysis results and illustrate the applicability of the proposed method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/21031.html} }
TY - JOUR T1 - A Decoupled, Parallel, Iterative Finite Element Method for Solving the Steady Boussinesq Equations AU - Hou , Yuanyuan AU - Yan , Wenjing AU - Boveleth , Lioba AU - He , Xiaoming JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 739 EP - 760 PY - 2022 DA - 2022/09 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/21031.html KW - Steady Boussinesq equations, decoupled parallel iterative algorithm, finite element method, error analysis. AB -

In this work, a decoupled, parallel, iterative finite element method for solving the steady Boussinesq equations is proposed and analyzed. Starting from an initial guess, an iterative algorithm is designed to decouple the Naiver-Stokes equations and the heat equation based on certain explicit treatment with the solution from the previous iteration step. At each step of the iteration, the two equations can be solved in parallel by using finite element discretization. The existence and uniqueness of the solution to each step of the algorithm is proved. The stability analysis and error estimation are also carried out. Numerical tests are presented to verify the analysis results and illustrate the applicability of the proposed method.

Hou , YuanyuanYan , WenjingBoveleth , Lioba and He , Xiaoming. (2022). A Decoupled, Parallel, Iterative Finite Element Method for Solving the Steady Boussinesq Equations. International Journal of Numerical Analysis and Modeling. 19 (6). 739-760. doi:
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