On the Existence Uniqueness and Numerical Computation of Non-linear Coupled Elliptic PDE System with its application

Abstract

In this study we prove the existence-uniqueness of a coupled non-linear elliptic PDE system using Lax-Milgram theorem, Galerkin Method, Brouwer's fixed point theorem. Later we derive the finite element scheme for the numerical solution of the PDE system and also carry out the convergence analysis for the derived scheme. Further successfully apply the scheme to an application related to free convection phenomena.