This project is based on combined efforts in discrete differential geometry and finite element methods for geometric partial differential equations. Especially, discretizations using polyhedral surfaces and piecewise linear functions on them proved to be very successful in both theory and applications. This development led to the creation of counterparts of geometric and metric properties of smooth surfaces on polyhedral surfaces and to insights on convergence properties of them. A geometric view onto finite element spaces of piecewise linear functions helped to develop a consistent theory of discrete differential forms on polyhedral surfaces.

Publications:

• Integration of generalized B-spline functions on Catmull–Clark surfaces at singularities, Anna Wawrzinek, Konrad Polthier, Computer Aided Design, (78), 2016, pp. 60-70
• On isoparametric Catmull-Clark finite elements for mean curvature flow, Anna Wawrzinek, Ph.D. thesis (submitted), 2016