Seminar in Numerical Analysis: Francois Bouchut (Université Paris-Est)
We study approximations by conforming methods of the solution to variational inequalities which arise in the context of inviscid incompressible Bingham type non-Newtonian fluid flows and of the total variation flow problem.
In the general context of a convex lower semi-continuous functional on a Hilbert space, we prove the convergence of time implicit space conforming approximations, without viscosity and for non-smooth data. Then we introduce a general class of total variation functionals, for which we can apply the regularization method. We consider the time implicit regularized, linearized or not, algorithms, and prove their convergence for general total variation functionals.
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