Course Details
Subject {L-T-P / C} : MA5360 : Finite Element Methods { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Snehashish Chakraverty
Syllabus
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.
Course Objectives
- To provide the fundamental concepts of the theory of the finite element method
Course Outcomes
1) to obtain an understanding of the fundamental theory of the FEA method <br />2) to develop the ability to generate the governing FE equations for systems governed by partial <br />differential equations <br />• Be able to derive equations in finite element methods for 1D, 2D and 3D problems. <br />• Be able to formulate and solve basic problems in heat transfer, solid mechanics and fluid mechanics. <br />• Be able to write computer program based on finite element methods. <br />• Be able to solve basic engineering problems in heat transfer, solid mechanics and fluid mechanics.
Essential Reading
- C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method,, Cambridge University Press, 1987. , Cambridge University Press, 1987.
- J. N. Reddy, An Introduction to Finite Element Method, McGraw Hill, 1993. , McGraw Hill, 1993.
Supplementary Reading
- C. A. J. Fletcher, Computational Galerkin Methods, Springer-Verlag, New-York inc, 1984. , Springer-Verlag, New-York inc, 1984.
- K. Erikssen et al., Computational Differential Equations, Cambridge University Press, 1996. , Cambridge University Press, 1996.