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

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Abstract

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.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China

    Demin Liu

  2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Kaitai Li

Authors
  1. Demin Liu
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  2. Kaitai Li
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Correspondence to Kaitai Li.

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Citation: LIU, D. M. and LI, K. T. Mixed finite element for two-dimensional incompressible convective Brinkman-Forchheimer equations. Applied Mathematics and Mechanics (English Edition), 40(6), 889–910 (2019) https://doi.org/10.1007/s10483-019-2487-9

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

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Liu, D., Li, K. Mixed finite element for two-dimensional incompressible convective Brinkman-Forchheimer equations. Appl. Math. Mech.-Engl. Ed. 40, 889–910 (2019). https://doi.org/10.1007/s10483-019-2487-9

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  • DOI: https://doi.org/10.1007/s10483-019-2487-9

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