Basic concept of the finite element method, Integral formulations and variational methods, The Lax-Milgram theorem, The abstract Galerkin method, Piecewise polynomial approximation in Sobolev spaces, Finite elements, Numerical quadrature, Applications to autonomous and non-autonomous problems, Optical error bounds in energy norms, Variational crimes, Apriori error estimates. The discontinuous Gaterkin methods, Adaptive finite element, The Autin-Nitscte duality argument, A posteriori error analysis.

To provide the fundamental concepts of the theory of the finite element method

1) to obtain an understanding of the fundamental theory of the FEA method
2) to develop the ability to generate the governing FE equations for systems governed by partial
differential equations
• Be able to derive equations in finite element methods for 1D, 2D and 3D problems.
• Be able to formulate and solve basic problems in heat transfer, solid mechanics and fluid mechanics.
• Be able to write computer program based on finite element methods.
• Be able to solve basic engineering problems in heat transfer, solid mechanics and fluid mechanics.

C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method,, Dover Publications , 2009

J. N. Reddy, An Introduction to Finite Element Method, McGraw Hill , 2006

S. Chakraverty, Nisha Rani Mahato, Perumandla Karunakar and Tharasi Dilleswar Rao, Advanced Numerical and Semi Analytical Methods for Differential Equations, Wiley , 2019

K. Erikssen et al., Computational Differential Equations, Cambridge University Press , 1996