Abstract:
This thesis focuses on solving two-dimensional elliptic partial differential
equations, namely the Laplace and Poisson equations, using the Galerkin finite
element method. Elliptic partial differential equation is a class of partial
differential equations describing phenomena that do not change from moment
to moment, as when a flow of heat or fluid takes place within a medium with
no accumulations. The Galerkin finite element method is a numerical technique
for solving partial differential equations. It is based on the idea of
approximating the exact solution of a PDE by a finite dimensional function
space spanned by a set of basis functions. MATLAB, a popular programming
language for technical computing, was used to implement the method and generate
the resulting figures and tables. The accuracy of the numerical results
was evaluated by comparing them to the exact solution, and the resulting error
demonstrated the effectiveness of the finite element method. Furthermore,
increasing the number of elements resulted in a reduction in the error, indicating
a convergence towards the exact solution
