PDE and Numerical Analysis seminar
Speaker: Amiya Pani, BITS Pilani, KK Birla Goa campus
Host: Harsha Hutridurga
Title: On Backward Time-Fractional Diffusion Problems: A Unified Approach
Time, day and date: 2:30:00 PM – 3:30:00 PM, Tuesday, October 06
Venue: Ramanujan Hall
Abstract: Inverse fractional diffusion problems, particularly backward problems, have received considerable attention in recent years. The resulting literature is diverse and sometimes fragmented, owing to the variety of models and numerical techniques employed. In this talk, we present a unified analysis of the quasi-boundary value method for solving backward problems associated with a broad class of time-fractional diffusion models. The regularized problem can be discretized using diverse spatial and temporal strategies. As a representative example, we analyze a piecewise linear finite element method in space, outline a rigorous error analysis for the semidiscrete scheme, and propose practical guidelines for selecting discretization and regularization parameters relative to the noise level. The unified nature of the analysis ensures its applicability to various fractional models, spatial discretizations, and more.

This is joint work with Samir Karaa and Mariam Al-Maskari (Sultan Qaboos University, Muscat, Oman).