ABSTRACT
It is known that finite difference methods are not very good at handling irregularly shaped domains. The finite element method can overcome this disadvantage. This chapter introduces the finite element method and related fundamental theory. It illustrates the finite element method through 1-D and 2-D examples, respectively. The chapter discusses some fundamental theory needed for analyzing the finite element method. It presents some commonly used conforming and nonconforming finite element spaces, respectively. Basic finite element interpolation theory is also introduced. The chapter reviews the error analysis for elliptic problems where both conforming and nonconforming elements are discussed. It also discusses the finite element method for parabolic equations.
