Sören Bartels (University of Freiburg)

Title: Error estimates for problems with pointwise constraints
Abstract: Various numerical methods for the approximation of partial differential equations with pointwise constraints have been developed within the last decades. Particular model problems include partial differential equations that characterize harmonic maps into spheres, variational problems arising in the nonlinear bending of thin elastic objects, and applications related to micromagnetics and liquid crystals. The numerical methods are often justified via weak compactness principles, i.e., that accumulation points of numerical approximations are exact solutions. Owing to a possible lack of regularity and uniqueness properties the deriviation of error estimates under meaningful conditions is challenging. The talk discusses optimality and limitations of different approaches.