Introduction to the Finite Element Method and Implementation with MATLAB®

Meshing is a process of discretizing a computational domain into a set of discrete elements with simple geometries. The non-overlapping elements combined represent the geometry of a computational domain. In addition, the elements are the small volumes where the physical quantities are approximated using simple mathematical functions, and the mesh of the elements ensures that the functions are stitched together piece by piece. Depending on the characteristics of the geometry and the type of the physical problem, the computational domains and elements can be categorized into 1-D, 2-D, and 3-D types. In this chapter, we first introduce some of the basic modeling and meshing concepts and techniques for different types of computational domains. Next, we focus on 2-D domains and describe in detail the modeling method of planar straight- line graphs and the meshing approach of Delaunay triangulation, and refinement for generating 2-D meshes of triangular elements.