Presynopsis Seminar
Speaker: Aamir Yousuf, IIT Bombay-Monash
Host:    Neela Nataraj
Title: New Discretizations for Coupled Multiphysics Models in Slender Geometries
Time, day and date: 11:30:00 AM - 1:00:00 PM, Friday, June 19
Venue: Ramanujan Hall (https://monash.zoom.us/j/87664111088?pwd=6wjE91IGhsBVrOf2UOicTMpapwoP5F.1)
Abstract: (https://drive.google.com/file/d/1xxllARz58CvuHm2go7oJ6RNz0FTT8SBL/view)

This talk addresses the numerical analysis of fourth-order partial differential equations (PDEs) arising in the modeling of thin and very thin elastic structures and coupled thermo-mechanical systems. Classical conforming finite elements for fourth-order problems, such as the Argyris element, require $C^1$-continuity across element boundaries, imposing significant implementation complexity and higher regularity demands on the solution. To overcome these difficulties, we employ nonstandard finite element methods, namely, the Morley, discontinuous Galerkin (dG), and $C^0$ interior penalty (C0IP) finite elements, which relax these continuity requirements while maintaining optimal approximation properties.

Three interconnected problem classes will be addressed in the talk. For the \textit{biharmonic wave equation}, we analyze explicit Leapfrog and implicit Newmark time-stepping schemes, establishing that explicit schemes suffer from a significantly more restrictive Courant--Friedrichs--Lewy (CFL) condition than classical second-order wave problems, and derive optimal error estimates via a modified Ritz projection on $H^2_0(\Omega)$. For the \textit{coupled thermoelastic diffusion and thermo-poroelastic systems}, a fourth-order hyperbolic equation for plate deflection is coupled with second-order parabolic equations for temperature and chemical potential (or pore pressure). A compatible combination of the Newmark and Crank--Nicolson schemes for the hyperbolic and parabolic components, respectively, yields quasi-optimal spatial convergence and quadratic temporal convergence.  For the \textit{dynamic von K\'{a}rm\'{a}n equations} governing geometrically nonlinear large deflections of very thin plates, the nonlinear coupling causes the classical Newmark scheme to lose unconditional stability. We resolve this through an energy-conserving discrete reformulation, establishing unconditional stability, existence and uniqueness of discrete solutions, and optimal a priori error estimates in the energy norm across all three nonstandard finite element frameworks. All theoretical findings are validated through numerical experiments.

Algebraic groups seminar
Speaker: Shripad M Garge, IIT Bombay
Title: Schur Weyl duality V
Time, day and date: 4:00:00 PM - 6:00:00 PM, Friday, June 19
Venue: Room No .105
Abstract: We complete our discussion on the Schur Weyl duality.