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.
High Order Whitney Forms on Simplices and the Question of Potentials / Rapetti, F.; Rodriguez, A. A.. - STAMPA. - 139:(2021), pp. 1-16. [10.1007/978-3-030-55874-1_1]
High Order Whitney Forms on Simplices and the Question of Potentials
Rapetti F.;Rodriguez A. A.
2021-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
