Courses

Course 01 (Elective) Mathematical Theory of Finite Element Methods: Quick tour to the theory of Distributions and essential elements of Sobolev Spaces, Variational formulation of elliptic boundary value problems, Lax-Milgram theorem, Error estimates, Construction of FE spaces, Polynomial approximations, interpolation errors, Aubin-Nitsche duality argument, Parabolic initial and boundary value problems: Semi-discrete and fully discrete schemes, error estimates.
Course 02 (Ph.D. level) Advance Topics in Functional Analysis and Applications: Theory of Distributions (Test space, Distributions, Basic operations, classification, Distributional derivatives, supports); Convolution ( of functions and of Distribution); Fundamental Solutions; Fourier Transform with properties; Fourier Inversion and Plancherel identity; Schwartz space and Tempered Distributions with applications; Sobolev spaces with properties (absolutely necessary ingredients); Fundamental Solution of Heat Equation.

References:

1. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer Verlag (2010).

2. S. Kesavan, Topics in Functional Analysis and Applications, New Age International (P) Ltd., New Delhi (2015).

3. W. Rudin, Functional Analysis, Tata McGraw-Hill,1974.

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