Finite element method

In this work, which is called "Finite Element Method", analysis of finite element method in one and two dimensional space is done. First; finite element method in one dimensional space is examined. Variational methods in approximation theory is examined and time dependent problems are studied. Moreover; having the variational formulation of the Poisson problem, we get the discrete equations. Also, error analysis in various norms is done. At the end of this section, some solved problems are given. Second; finite element method in two dimensional space is examined. During finite element discretization, we get local discrete equations belonging to an indiviual element. By assembly procedure global equation system is attained. According to boundary conditions the difference in the equations is examined. At the end of this section, some solved problems in two dimensional space are given. Keywords: Finite element, strong formulation, rninimization principle, weak solution, variational problem, elliptic problem.