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 - <p style="text-align: justify;">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.</p>