Mixed finite element for two-dimensional incompressible convective Brinkman-Forchheimer equations  

作　　者：Demin LIU Kaitai LI 

机构地区：[1]College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China [2]School of Mathematics and Statistics,Xi’an Jiaotong University,Xi’an 710049,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2019年第6期889-910,共22页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11461068,11362021,and 11401511);the Doctoral Foundation of Xinjiang Uygur Autonomous Region of China(No.BS110101)

摘　　要：In this work, the two-dimensional convective Brinkman-Forchheimer equa- tions are considered. The well-posedness for the variational problem and its mixed finite element approximation is established, and the error estimates based on the conforming approximation are obtained. For the computation, a one-step Newton (or semi-Newton) iteration algorithm initialized using a fixed-point iteration is proposed. Finally, numerical experiments using a Taylor-Hood mixed element built on a structured or unstructured triangular mesh are implemented. The numerical results obtained using the algorithm are compared with the analytic data, and are shown to be in very good agreement. Moreover, the lid-driven problem at Reynolds numbers of 100 and 400 is considered and analyzed.In this work, the two-dimensional convective Brinkman-Forchheimer equations are considered. The well-posedness for the variational problem and its mixed finite element approximation is established, and the error estimates based on the conforming approximation are obtained. For the computation, a one-step Newton(or semi-Newton)iteration algorithm initialized using a fixed-point iteration is proposed. Finally, numerical experiments using a Taylor-Hood mixed element built on a structured or unstructured triangular mesh are implemented. The numerical results obtained using the algorithm are compared with the analytic data, and are shown to be in very good agreement. Moreover,the lid-driven problem at Reynolds numbers of 100 and 400 is considered and analyzed.

关 键 词：Brinkman-Forchheimer EQUATIONS finite element method NEWTON ITERATION 

分 类 号：O241.8[理学—计算数学] O242.1[理学—数学]