Application of the Chimera Method to Poisson’s Equation with the Homogeneous Dirichlet Boundary Condition

Abstract

Establishing variational formulation is an effective way to study the existence and uniqueness of the solution of certain elliptic partial differential equation with boundary condition. For the solution of certain elliptic partial differential equation with boundary condition, we know that the numerical solution obtained by the finite element method approximates the solution of this equation. Moreover, to avoid gridding overly complex domains, we can use the Chimera method to decompose the domain into several overlapping sub-domains. In this paper, we study Poisson’s equation with the homogeneous Dirichlet boundary condition. By analyzing the existence and uniqueness of the solution of the corresponding variational formulation, we know the existence and uniqueness of the solution of Poisson’s equation with the homogeneous Dirichlet boundary condition. We use the Chimera method and the finite element method to deal with Poisson’s equation with the homogeneous Dirichlet boundary condition by constructing two iterative sequences and analyzing their properties.