ABSTRACT
The physical processes encountered in all branches of sciences and engineering can be classified into two categories: time-dependent processes and stationary processes. Time-dependent processes describe evolutions in which quantities of interest change as time elapses. A mathematical description of most stationary processes in sciences and engineering often leads to a system of ordinary or partial differential equations. The mathematical descriptions of the stationary processes are referred to as boundary value problems (BVPs). When addressing numerical solutions of BVPs using the finite element method, the domain of definition Ω¯ over which the BVP is defined is subdivided into smaller domains called subdomains. Once we have the numerical values of the degrees of freedom at the grid points and thus at the node points of each element, the element local approximation provides an analytical expression for the behaviors of the dependent variables over each element.
