Abstract
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