Finite Elements Method for Solving Elliptic and Hyperbolic Partial Differential Equations

In various disciplines of engineering such as hydrodynamics, heat conduction, geomechanics, civil engineering, nuclear, and even biomedical, the finite element method (FEM) is known to be an effective and sophisticated technique to tackle complex computational problems. The main idea of FEM is to break down a complicated space or domain into a number of small, countable, and finite elements, or “finite elements” by approximation methods whose behavioral outputs could be predicted using simpler equations. In this work, we will analyze the comparison between the Finite Difference Method (FDM) and FEM in order to see the effectiveness of each method. Within the scope of this research, several types of partial differential equations (PDEs) will be solved with FEM to estimate a solution that is as accurate as possible to the exact answer. Computations will be completed with the MATLAB software, and a discussion will follow.