H^m non-conforming finite element spaces on polygonal meshes in arbitrary dimensions

by Shudan Tian (Xiangtan University)

Tuesday 28 Jul 2026, 10:15 → 11:15 Europe/Berlin

tba (Inselplatz 5)

In this talk, I will introduce a non-conforming element method for 2m-th order elliptic problems in arbitrary dimensions on polygonal meshes.
This construction is based on the Staggered Discontinuous Galerkin (SDG) method. We consider a mixed formulation where the tensor σ​ and the displacement u​ are discretized on two different meshes. This approach relaxes the continuity requirements for σ. Moreover, we propose a geometric decomposition for m-th order symmetric tensors, which is crucial for proving the inf‑sup condition.
The method can be viewed as a non‑conforming element scheme that places all degrees of freedom on (d–1)-dimensional faces, making it straightforward to implement. A large number of degrees of freedom can be condensed within the SDG framework. Finally, numerical experiments validate our theoretical findings.