Author(s)

George Papanikos, Maria Ch. Gousidou-Koutita

School of Mathematics, Aristotle University, Thessaloniki, Greece.

In this paper, we consider two methods, the Second order Central Difference Method (SCDM) and the Finite Element Method (FEM) with P₁ triangular elements, for solving two dimensional general linear Elliptic Partial Differential Equations (PDE) with mixed derivatives along with Dirichlet and Neumann boundary conditions. These two methods have almost the same accuracy from theoretical aspect with regular boundaries, but generally Finite Element Method produces better approximations when the boundaries are irregular. In order to investigate which method produces better results from numerical aspect, we apply these methods into specific examples with regular boundaries with constant step-size for both of them. The results which obtained confirm, in most of the cases, the theoretical results.

Finite Element Method, Finite Difference Method, Gauss Numerical Quadrature, Dirichlet Boundary Conditions, Neumann Boundary Conditions

Papanikos, G. and Gousidou-Koutita, M. (2015) A Computational Study with Finite Element Method and Finite Difference Method for 2D Elliptic Partial Differential Equations. Applied Mathematics, 6, 2104-2124. doi: 10.4236/am.2015.612185.