Research Projects

Liquid crystals, transitional phases between liquid and crystalline phases, have versatile properties and are used in various applications. Pierre-Gilles de Gennes won the Nobel Prize in Physics in 1991 for generalizing order phenomena to more complex forms of matter. This project aims to analyze finite element methods for nonlinear models, including thermotopic and ferronematics phases. The project aims to improve a posteriori estimates and reduce/saturation for conforming, nonconforming, and discontinuous Galerkin finite element methods (dGFEM) in the context of nonlinear problems. The German PI, an international leader in adaptive FEM, will help improve preliminary results on a posteriori estimates. The project also aims to fill the gap of adaptive convergence by capturing the h-ε dependency in a posteriori estimate. The project also explores mixed methods, such as the Raviart-Thomas mixed finite element method and the Crouzeix-Raviart nonconforming finite element method, which are efficient schemes for optimal design problems in topology optimization. The German group will also develop software libraries for conforming, nonconforming, dGFEMs, and adaptive FEMs for semi-linear problems. The project will also involve outreach activities and funding from Indian organizations.