MA 347A: Topics in Finite Element Methods
Credits: 3:1
Prerequisite courses: UM101, UM102, UM204
Prerequisites :
- Topics from MA 222, MA 223 and MA242 are desirable but not absolutely necessary.
Weak derivative, Sobolev spaces. Triangulation, finite element construction, interpolation estimates. Conforming finite elements, non-conforming finite elements, mixed methods, discontinuous Galerkin methods and polygonal mesh methods for solving PDEs. Solving time dependent PDEs by using finite differences in time and finite elements in space. Lab component consisting of MATLAB implementation of these methods.
Note: This course is essentially for the BTech Math and Computing students in their third or fourth year. But it can also be taken by BS students (Math Majors/minors) and integrated PhD students from Mathematics department. Any MTech/PhD student from the institute who needs to solve differential equations can also take it.
Suggested books and references:
- C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover Publications, New York, 2009.
- Alexandre Ern and J.-L. Guermond, Theory and Practice of Finite Elements, vol. 159 of Applied Mathematical Series, Springer, New York, 2004.
- P. G. Ciarlet, Lectures on Finite Element Method, TIFR Lecture Notes Series, Bombay (1975).
- J. N. Reddy, An introduction to the Finite Element Method, McGraw-Hill, Inc., 1993..