Cubic Lagrange elements satisfying exact incompressibility
arXiv:1712.0067217 citationsh-index: 32
AI Analysis
Provides a theoretical foundation for exactly divergence-free finite element methods in computational fluid dynamics, addressing a known bottleneck in the field.
The paper proves that cubic Scott-Vogelius finite elements are inf-sup stable on nondegenerate meshes, enabling exact incompressibility for Stokes flow. It also characterizes the divergence space and links it to C^1 piecewise quartics.
We prove that an analog of the Scott-Vogelius finite elements are inf-sup stable on certain nondegenerate meshes for piecewise cubic velocity fields. We also characterize the divergence of the velocity space on such meshes. In addition, we show how such a characterization relates to the dimension of C^1 piecewise quartics on the same mesh.