@inproceedings{a8a4a2d1226e4bf98a1d90a7734a239b,
title = "The finite element method and its' link to the finite difference method for poisson's equation",
abstract = "Poisson's Equation on a rectangular domain describes conduction heat transfer on a plate. This equation can be solved using the Finite Difference Method (FDM) or the Finite Element Method (FEM). Previous literature has shown that the FEM discretisation equations for the nodal values are integrated averages of the FDM discretisation equations. This paper presents a corrected transformation from the FDM to the FEM, for Poisson's Equation. For Poisson's Equation on a rectangular domain the FEM discretisation is obtained by the area integral, in terms of Simpson's and Midpoint Quadrature, of the FDM discretisation equations. Under the conditions investigated in this paper, the FEM provides the area integral of the partial differential equation (PDE) in terms of Simpson's and Midpoint Quadrature. The transformation presented in this paper can be used to reduce computational cost and complexity in the FEM, specifically in the construction of the discretisation equations at the nodal points.",
keywords = "Area integral, Finite difference method, Finite element method, Midpoint quadrature, Poisson's equation, Simpson's quadrature",
author = "Muaaz Bhamjee and Alan Nuricky",
note = "Publisher Copyright: {\textcopyright}SACAM 2012.; 8th South African Conference on Computational and Applied Mechanics, SACAM 2012 ; Conference date: 03-09-2012 Through 05-09-2012",
year = "2012",
language = "English",
series = "8th South African Conference on Computational and Applied Mechanics, SACAM 2012 - Conference Proceedings",
publisher = "South African Association for Theoretical and Applied Mechanics (SAAM)",
pages = "148--153",
editor = "Nel, {Andre Leon} and {Janse van Rensburg}, Nickey and Madyira, {Daniel M.}",
booktitle = "8th South African Conference on Computational and Applied Mechanics, SACAM 2012 - Conference Proceedings",
}