Numerical Approximation of the Ericksen Leslie Equations
AbstractThe Ericksen Leslie equations model the motion of nematic liquid crytaline fluids. The equations comprise the linear and angular momentum equations with non-convex constraints on the kinematic variables. These equations possess a Hamiltonian structure which reveals the subtle coupling of the two equations, and a delicate balance between inertia, transport, and dissipation. While a complete theory for the full nonlinear system is not yet available, many interesting sub-cases have been analyzed.
This talk will focus on the development and analysis of numerical schemes which inherit the Hamiltonian structure, and hence stability, of the continuous problem. In certain situations compactness properties of the discrete solutions can be established which guarantee convergence of schemes.