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Existence and Uniqueness of Generalized and Mixed Finite Element Solutions for Steady Boussinesq Equation

Author

Listed:
  • Zhendong Luo

    (School of Digitalized Intelligence Engineering, Hunan Sany Polytechnic College, Changsha 410129, China)

  • Xiangdong Liu

    (School of Digitalized Intelligence Engineering, Hunan Sany Polytechnic College, Changsha 410129, China)

  • Yihui Zeng

    (School of Digitalized Intelligence Engineering, Hunan Sany Polytechnic College, Changsha 410129, China)

  • Yuejie Li

    (Department of Mathematics and Computer Engineering, Ordos Institute of Technology, Ordos 017000, China)

Abstract

Herein, we mainly employ the fixed point theorem and Lax-Milgram theorem in functional analysis to prove the existence and uniqueness of generalized and mixed finite element (MFE) solutions for two-dimensional steady Boussinesq equation. Thus, we can fill in the gap of research for the steady Boussinesq equation since the existing studies for the equation are assumed the existence and uniqueness of generalized solution without providing proof.

Suggested Citation

  • Zhendong Luo & Xiangdong Liu & Yihui Zeng & Yuejie Li, 2023. "Existence and Uniqueness of Generalized and Mixed Finite Element Solutions for Steady Boussinesq Equation," Mathematics, MDPI, vol. 11(3), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:545-:d:1041596
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    References listed on IDEAS

    as
    1. Gennady Alekseev & Dmitry Tereshko, 2011. "Stability of Optimal Controls for the Stationary Boussinesq Equations," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-28, November.
    2. Evgenii S. Baranovskii, 2021. "Optimal Boundary Control of the Boussinesq Approximation for Polymeric Fluids," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 623-645, May.
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