Finite Element Approximations for One and Two Dimensional Boundary-ValueProblems

Abstract

The finite element method is a technique for systematic- ally applying Galerkin's method to the approximate solution of boundary-value problems. In this thesis we construct a variati- onal formulation of one-dimensional value problems, Galerkin approximation and we discuss modifications in these terms for different types of boundary conditions subsequently for one-dimensional problems. We generalized it to a two-dimensional problems. We show for the finite element interpolation how to partitioning the domain and how to construct and select shape functions to the approximate solution of boundary-value problem on triangle and rectangular elements.We discuss modifications in these terms for different types of boundary conditions subsequently for one-dimensional problem. Finally a linear interpolation by using shape functions and boundary conditions are constructed on triangular and rectangular elem- ents.