Introduction and motivation, Weak formulation of BVP and Galerkin approximation, Piecewise polynomial spaces and finite element method, Computer implementation of FEM, Results from Sobolev spaces, Variational formulation of elliptic BVP, LaxMilgram theorem, Estimation for general FE approximation, Construction of FE spaces, Polynomial approximation theory in Sobolev spaces, Variational problem for second order elliptic operators and approximations, Mixed methods, Iterative techniques. 
Text/Reference Books:
 Susanne C. B., Ridgway S., The Mathematical Theory of Finite Element Methods, Springer
 Reddy J. N. Introduction to Finite Element Methods, McGrawHill
 Hughes T. J.R. The Finite Element Method, Dover Publications
 Zienkiewicz O. C. The Finite Element Method, Tata McGrawHill
