A Family of Crouzeix-Raviart Non-Conforming Finite Elements in Two- and Three Spatial Dimensions

Explore a comprehensive lecture on Crouzeix-Raviart non-conforming finite elements in two and three spatial dimensions. Delve into the family of elements consisting of local polynomials of maximal degree p on simplicial finite element meshes, with imposed jump conditions across adjacent simplices. Learn about optimal a priori estimates, the historical context of Crouzeix and Raviart's 1973 paper, and the challenges in deriving explicit representations of local basis functions for general p in 3D. Discover the development of theoretical tools for fully symmetric and reflection symmetric orthogonal polynomials on triangles and their representations. Analyze the linear independence of these function sets and discuss their potential to span the entire non-conforming space. Gain insights from this collaborative work involving experts from ENSTA Paris and Virginia Tech, presented within the Hausdorff Trimester Program on Multiscale Problems.