European Numerical Mathematics and
Advanced Applications Conference 2019
30th sep - 4th okt 2019, Egmond aan Zee, The Netherlands
09:15   Zuiderduinzaal: Keynote: Francesca Rapetti, Laboratoire de Mathematiques Dieudonne, France
45 mins
High order Whitney forms on simplices and the question of potentials
Francesca Rapetti, Ana Alonso Rodriguez
Abstract: In the frame of high order finite element approximations of PDEs, we are interested in an explicit and efficient way for constructing finite element functions with assigned gradient, curl or divergence in domains with general topology. Three ingredients, that bear the name of their scientific fathers, are involved: the de Rham's diagram and theorem, Hodge's decomposition for vectors, Whitney's differential forms. Some key images are presented in order to illustrate the mathematical concepts.