In finite element method, We need to make a grid of problem space, assemble stiffness matrix , global matrix and right hand side vector to obtain a linear system.
Then use numerical methods to solve the linear system to find the numerical solution.
In this paper we use DEAL.II library to programming the finite element method to find a numerical solution.

1 Introduction 1
2 Finite element method for eliliptic problem 1
3 Finite element method for hyperbolic problem 5
3.1 Standard Galerkin method . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 The discontinuous Galerkin method . . . . . . . . . . . . . . . . . . . 8
4 Deal.II 10
4.1 Create a grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2 Solving the problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.3 Data output and graphic the solution. . . . . . . . . . . . . . . . . . 16
4.4 Example of programming . . . . . . . . . . . . . . . . . . . . . . . . . 18
5 Examples 29
References 50

ibitem {Johnson} Claes Johnson, extit{Numerical solution of partial differential equations by the finite elements method},
CAMBRIDGE UNIVERSITY PRESS
ibitem {Strauss} Walter A. Strauss, extit{Parial differental equations an introduction}
ibitem {Deal.II} Deal.II Team, extit{Deal.II} , Homepage: http://www.dealii.org