Kaibo Hu, Associate Professor, University of Oxford

Shipeng Mao, Professor&Shuo Zhang, Associate Professor

Finite element tensor calculus-Lecture 2

9:00-11:00 December 4(Thursday), N224

This short course aims to provide an overview of recent advances in differential complexes and vector- and tensor-valued finite elements, with applications to structure-preserving and compatible discretizations in fluid and solid mechanics and differential geometry.

At the continuous level, we investigate de Rham complexes and the Bernstein-Gelfand-Gelfand (BGG) machinery, emphasizing their role in modeling generalized continua. At the discrete level, we introduce a canonical discretization of form-valued forms (double forms), covering various discrete differential geometric schemes and finite element methods for fluid and solid mechanics.