Numerical Solution of Two Dimensional Poisson and Laplace Equations
1 Department of Statistics and Mathematical Sciences Kwara State University, Malete, Nigeria
2 Department of Mathematics, University of Ilorin, Nigeria;
3 Department of Computational and Applied Mathematics, The University of Witwatersrand, Johannesburg, South Africa.
* Corresponding author: aliutajudeen@njmajournal.com.ng
2 Department of Mathematics, University of Ilorin, Nigeria;
3 Department of Computational and Applied Mathematics, The University of Witwatersrand, Johannesburg, South Africa.
* Corresponding author: aliutajudeen@njmajournal.com.ng
Abstract
The study identifies the use of Finite Element Method with
both rectangular and Triangular elements in solving two di
mensional problems with Dirichlet boundary condition in a
rectangular domain. We use the product functions of linear
polynomial basis constructed by (Aliu & Bamigbola, 2014)
on the rectangular elements. Attempt was made at con
structing the basis functions for Triangular elements. The
Finite Difference scheme was also used for comparison. The
results obtained using both the rectangular and triangular
elements via the finite element method and the Central Fi
nite Difference Scheme compared favourably with the exact
solution. The rectangular element however gives a better
approximation.
Keywords
Finite Difference scheme
Dirichlet boundary condition
Basis Function
and Quadrilateral Elements
How to Cite
Tajudeen, A., Bamigbola, O. M., & Ali, A. M. (2017). Numerical Solution of Two Dimensional Poisson and Laplace Equations. Nigerian Journal of Mathematics and Applications, 26(1), 95 −112.
A. Tajudeen, O. M. Bamigbola, and A. M. Ali, "Numerical Solution of Two Dimensional Poisson and Laplace Equations," Nigerian Journal of Mathematics and Applications, vol. 26, no. 1, pp. 95 −112, September 2017.
