Student APS
Speaker: Shivani, IIT Bombay
Host: Neela Nataraj
Title: Discontinuous Galerkin finite element methods for linear and semilinear fourth-order problems in smectic liquid crystals
Time, day and date: 2:00:00 PM – 3:00:00 PM, Wednesday, February 18
Venue: Ramanujan Hall
Abstract: In this talk, we will discuss the analysis and numerical approximation of a regular solution to a semilinear fourth-order partial differential equation defined on a polygonal domain, modelling the density variation of Smectic-A liquid crystals. First, we will discuss the discontinuous Galerkin finite element method for the corresponding linear problem. Building upon this, we will discuss the analysis of the semilinear fourth-order problem. For the nonlinear model, we establish existence, local uniqueness, and optimal order error estimates in the energy norm under the assumption that the exact solution $u\in H^{2+\alpha}(\Omega)$ with $\alpha>0$. Numerical experiments validating the theoretical results will also be presented.