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

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 Boussi...

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Published inMathematics (Basel) Vol. 11; no. 3; p. 545
Main Authors Luo, Zhendong, Liu, Xiangdong, Zeng, Yihui, Li, Yuejie
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2023
Subjects
Boussinesq equations
existence and uniqueness of generalized solution
existence and uniqueness of mixed finite element solution
Existence theorems
Finite element method
Fixed point theory
Fixed points (mathematics)
Functional analysis
Inequality
Mathematical research
Navier-Stokes equations
Numerical analysis
Reynolds number
the fixed point theorem
the Lax-Milgram theorem
Theorems
Uniqueness
Water waves
Wave equation
China
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ISSN2227-7390
2227-7390
DOI10.3390/math11030545

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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math11030545