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

Zhendong Luo, Xiangdong Liu, Yihui Zeng and Yuejie Li ()
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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

Mathematics, 2023, vol. 11, issue 3, 1-14

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.

Keywords: the fixed point theorem; the Lax-Milgram theorem; existence and uniqueness of generalized solution; existence and uniqueness of mixed finite element solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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