Ph.D. Defence
Speaker: Mr. Rishi Das, IIT Bombay
Host: Harsha Hutridurga
Title: Robust Mathematical Analysis and Numerical Methods for Flow-Transport Problems
Time, day and date: 4:00:00 PM – 5:00:00 PM, Wednesday, October 07
Venue: Ramanujan Hall (https://zoom.us/j/92827897299?pwd=55qKZRjyi6JM8dPTupMAGekskLkkk3.1)
Abstract: Mixed finite element methods naturally give rise to saddle-point structures. We exploit this intrinsic structure to construct parameter-dependent weighted spaces and establish robust well-posedness for three models arising in fluid flow and transport through porous media: the Darcy system, the Darcy—Forchheimer system, and the coupled Darcy--Forchheimer and advection-diffusion-reaction system. For each model, we develop parameter-robust discretization, derive a priori error estimates with constants independent of the physical parameters, and construct robust block-diagonal preconditioners within the operator preconditioning framework. Numerical results illustrate the robustness of the proposed methods across a wide range of physically relevant parameter regimes.