Department of Mathematics

INDIAN INSTITUTE OF SCIENCE

MA 347: Advanced Partial Differential Equations and Finite Element Method

Credits: 3:0

Distribution Theory - Introduction, Topology of Test functions, Convolutions, Schwartz Space, Tempered Distributions, Fourier Transform;

Sobolev Spaces - Definitions, Extension Operators, Continuous and Compact Imbeddings, Trace results; Weak Solutions - Variational formulation of Elliptic Boundary Value Problems, Weak solutions, Maximum Principle, Regularity results;

Finite Element Method (FEM) - Introduction to FEM, Finite element solution of Elliptic boundary value problems.  

Suggested books and references:

1. L. Schwartz, Theorie des Distributions, Hermann, (1966).
2. S. Kesavan, Topics in Functional Analysis and applications, John Wiley & Sons (1989).
3. P. G. Ciarlet, Lectures on Finite Element Method, TIFR Lecture Notes Series, Bombay (1975).
4. J. T. Marti, Introduction to Finite Element Method and Finite Element Solution of Elliptic Boundary Value Problems, Academic Press (1986).

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