On Friday, March 31, 2023, Prof. Dr. Endre Süli (University of Oxford) will give a talk entitled "Discrete De Giorgi-Nash-Moser Theori: Analysis and Applications" starting at 12:30 p.m. in Room 706 of the Faculty of Mathematics.
Abstract:
The talk is concerned with a large class of numerical methods for
the approximate solution of a system of nonlinear elliptic partial differential equations that arise in models of chemically-reacting
viscous incompressible non-Newtonian fluids. In order to prove the
convergence of the numerical method under consideration one needs to
derive a uniform Hölder norm bound on the sequence of approximations
in a setting where the diffusion coefficient in the convection-diffusion
equation involved in the system is merely a bounded function with no
additional regularity. This necessitates the development of a discrete
counterpart of De Giorgi’s elliptic regularity theory, which is then
used, in combination with various weak compactness techniques, to
deduce the convergence of the sequence of numerical solutions to a
weak solution of the system of partial differential equations. The
theoretical result are illustrated by numerical experiments for a
model of the synovial fluid, a non-Newtonian chemically-reacting
incompressible fluid contained in the cavities of human joints.