Numerical approximation of complex fluids: compactness properties and open questions

Thursday, February 25, 2010 - 4:30pm - 5:15pm
EE/CS 3-180
Keywords: Complex Fluids, Complactness

Abstract: A classical result of P. Lax states that a (linear) numerical
scheme converges if and only if it is stable and consist. For nonlinear
problems this statement needs to augmented to include a compactness hypotheses
sufficient to guarantee convergence of the nonlinear terms. This talk will
focus on the development of numerical schemes for parabolic equations that are
stable and inherit compactness properties of the underlying partial
differential equations. I will present a discrete analog of the classical
Lions-Aubin compactness theorem and use it to establish convergence of
numerical schemes for fluids transporting membranes, and the Ericksen Leslie
equations for (nematic) liquid crystals. The talk will finish with some open
problems that arise in the numerical simulation of this class of problems.
MSC Code: