Mathematics (Jan 2023)

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

  • Zhendong Luo,
  • Xiangdong Liu,
  • Yihui Zeng,
  • Yuejie Li

DOI
https://doi.org/10.3390/math11030545
Journal volume & issue
Vol. 11, no. 3
p. 545

Abstract

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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