Annual Progress Seminar
Speaker: Aamir Yousuf (IIT Bombay)
Host: Neela Nataraj
Title: Numerical analysis of a thermoelastic diffusion plate model
Time, day and date: 11:00:00 AM, Monday, February 24
Venue: Online (Link in attached file)
Abstract: We investigate the well-posedness of a coupled
hyperbolic-parabolic system modeling diffusion in thermoelastic plates,
consisting of a fourth-order hyperbolic PDE for plate deflection and
second-order parabolic PDEs for the first moments of temperature and
chemical potential. The unique solvability is established via the
Galerkin approach, and additional regularity of the solution is obtained
under appropriately strengthened given data. For numerical
approximation, we employ the Newmark method for time discretization and
a C 0 -interior penalty (C0-IP) scheme for the spatial discretization of
displacement. For the first moments of temperature and chemical
potential, we use the Crank-Nicolson method for time discretization and
conforming finite elements for spatial discretization. The convergence
of the fully discrete scheme is established, achieving quasi-optimal
rates in space and a quadratic rate in time. Several numerical examples
will be presented to validate the theoretical findings.