Hi, I am V Santhanakumar, a research scholar in the Department of Mathematics at IIT Guwahati, working under the supervision of Prof. Natesan Srinivasan. My research focuses on the development and rigorous analysis of numerical methods for fractional partial differential equations and singularly perturbed problems, with particular emphasis on finite element and discontinuous Galerkin methods. I also explore physics-informed neural networks for solving partial differential equations.