ABSTRACT
Knowing that polynomial-based approximate solutions can sometimes provide very satisfying solutions to differential equations, one may wonder if such an approximate-solution-finding procedure based on polynomial functions can be handled by a computer program. Finite element method (FEM), which is also known as finite element analysis, is exactly one such computerized numerical procedure for finding approximate solutions to a wide range of scientific and engineering problems. Depending on the spacial dimensions of a physical domain, the finite elements can take various shapes and sizes of different dimensions. In general, for one-dimensional structures elements are line segments, for two-dimensional structures elements can be triangles or quadrilaterals, and for three-dimensional structures elements can be tetrahedrons, hexahedrons, and so on. Nodes are very important in FEM. Aside from providing connections between neighboring elements, nodes are where the geometric information of the physical domain is passed to the elements through the coordinates of nodes.
