SAYAS NUMERICS SEMINAR     Register to attend talk
September 7, 2021 at 3:30pm (Eastern Time)

Nonconforming and Discontinuous Methods in the Numerical Approximation of Nonsmooth Variational Problems

Sören Bartels
University of Freiburg

Nonconforming and discontinuous finite elements are attractive for discretising variational problems with limited regularity properties, in particular, when discontinuities may occur. The possible lack of differentiability of related functionals prohibits the use of classical arguments to derive error estimates.

As an alternative we make use of discrete and continuous convex duality relations and of quasi-interpolation operators with suitable projection properties. For total variation regularised minimisation problems a quasi-optimal error estimate is derived which is not available for standard finite element methods. Our results use and extend recent ideas by Chambolle and Pock.