Estimating the error between analytical and numerical finite difference solutions of laplace equation

Abstract

This work presents an estimation method for the calculation of the error between numerical and analytical solutions of the Laplace Equation. The study is performed by obtaining general estimates for the exact error of the numerical difference equation. The method is based on the polynomial approximation of the error using relative dimension simulations. The work is validated by comparison between the discrete solutions and numerical results, and with general problems.