Mathematical and Numerical Analysis for Neumann Boundary Value Problem of the Poisson Equation

This paper falls within the framework of mathematical modelling and that of numerical analysis. The analysis to be developed through this paper deals with three Neumann boundary value problmes: one pure, one modified and the other with conduction term for the Poisson equation. We introduced Dirichlet and Neumann problems with conduction valuables to prove the continuity in comparison with conduction term of the Neumann problem. We demonstrated the existence and uniqueness of the modified Neumann problem. For simplicity and concreteness, it was appropriate to choose the finite element and classical methods to find the numerical and the explicit solutions, respectively so that numerical simulations were implemented in Scilab.