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

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