Finite Element Methods for Partial Differential Equations

Code: MA671 | L-T-P-C: 3-0-0-6

Prerequisites: MA322/MA572 or equivalent

Basic concepts of finite element methods; Elements of function spaces, Lax-Milgram theorem, piecewise polynomial approximation in function spaces, Galerkin orthogonality and Cea’s lemma, Bramble-Hilbert lemma, Aubin-Nitsche duality argument; Applications to elliptic, parabolic and hyperbolic equations, a priori error estimates, variational crimes; A posteriori error analysis – reliability, efficiency and adaptivity.

Texts/References:

1. C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover Publications, 2009.
2. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, 1978.
3. J. N. Reddy, An Introduction to Finite Element Method, McGraw Hill, 1993.
4. S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods, 2nd edition, Springer, 2002.
5. Z. Chen, Finite Element Methods and Their Applications, Springer, 2005.
6. D. L. Logan, A First Course in the Finite Element Method, 4th edition, Cenegage Learning India Pvt Ltd, 2007.
7. A. J. Davies, The Finite Element Method: An Introduction with Partial Differential Equations, Oxford University Press, 2011.